Middlebury: Faculty & Office Hours
http://www.middlebury.edu/academics/math/faculty
enPriscilla Bremser
http://www.middlebury.edu/academics/math/faculty/node/26431
<div class="field field-name-field-features field-type-list-text field-label-above"><div class="field-label">Dynamic Features: </div><div class="field-items"><div class="field-item even">Course Catalog</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Degrees, Specializations & Interests:</strong><br /><span>A.B., Smith College; M.A., Ph.D., Johns Hopkins University. Research in Number Theory, Finite Fields, and Mathematics Education.</span></p>
<p> </p>
<p><strong>Blog<br /></strong><a href="http://mathsugaroff.wordpress.com/">http://mathsugaroff.wordpress.com/</a></p>
<p> </p></div></div></div><div class="field field-name-field-extras field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p><a href="http://mathsugaroff.wordpress.com/"></a> </p></div></div></div><div class="field field-name-field-user field-type-user-reference field-label-above"><div class="field-label">User: </div><div class="field-items"><div class="field-item even"><a href="/user/4940">Priscilla Bremser bremser@middlebury.edu</a></div></div></div><div class="field field-name-field-feeditems field-type-list-integer field-label-above"><div class="field-label">Items per Feed: </div><div class="field-items"><div class="field-item even">2</div></div></div><div class="field field-name-middlebury-course-list field-type-middlebury-course-list-courses field-label-above"><div class="field-label">Course List: </div><div class="field-items"><div class="field-item even">
<p>Courses offered in the past four years. <br/><span title="Offered in the current term">▲</span> <em>indicates offered in the current term</em><br/><span title="Offered in the upcoming term[s]">▹</span> <em>indicates offered in the upcoming term[s]</em></p>
<h5 class='coursetitle'>FYSE 1212 - Mathematics For All
</h5>
<div class='coursedesc'>
<p><strong>Mathematics for All</strong><br />
What kinds of mathematical knowledge are necessary for full participation in contemporary democratic society? How well, and how fairly, do our schools educate students in quantitative skills and reasoning? By what measures might we judge success? We will learn about different approaches to mathematics education in light of these questions. Readings will include selections from <em>Mathematics for Democracy: The Case for Quantitative Literacy</em> (L.A. Steen, Editor), as well as recent articles by education researchers. To connect theory and actual practice, students in this class will conduct a service-learning project in a local school. All are welcome, regardless of mathematical background. 3 hrs. sem. <strong>CW</strong>
</p>
<p>Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FFYSE1212">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0109 / EDST 0109 / EDST 1005 / MATH 1005 - Mathematics for Teachers
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Mathematics for Teachers</strong><br />
What mathematical knowledge should elementary and secondary teachers have in the 21st century? Participants in this course will strengthen and deepen their own mathematical understanding in a student-centered workshop setting. We will investigate the number system, operations, algebraic thinking, measurement, data, and functions, and consider the attributes of quantitative literacy. We will also study recent research that describes specialized mathematical content knowledge for teaching. (Not open to students who have taken MATH/EDST 1005. Students looking for a course in elementary school teaching methods should consider EDST 0315 instead.) <strong>DED</strong>
</p>
<p>Winter 2012, Spring 2014, Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0109">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0121 - Calculus I
</h5>
<div class='coursedesc'>
<p><strong>Calculus I</strong><br />
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2014, Fall 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0121">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0122 - Calculus II
</h5>
<div class='coursedesc'>
<p><strong>Calculus II</strong><br />
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2011</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0122">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0200 - Linear Algebra
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Linear Algebra</strong><br />
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2012, Spring 2015, Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0200">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0241 - Elementary Number Theory
</h5>
<div class='coursedesc'>
<p><strong>Elementary Number Theory</strong><br />
Divisibility and prime factorization. Congruences; the theorems of Lagrange, Fermat, Wilson, and Euler; residue theory; quadratic reciprocity. Diophantine equations. Arithmetic functions and Mobius inversion. Representation as a sum of squares. (MATH 0122 or by waiver) <strong>DED</strong>
</p>
<p>Fall 2011</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0241">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0302 - Abstract Algebra I
</h5>
<div class='coursedesc'>
<p><strong>Abstract Algebra</strong><br />
Groups, subgroups, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, rings and ideals, integral domains and fields, the field of quotients of a domain, the ring of polynomials over a domain, Euclidean domains, principal ideal domains, unique factorization, factorization in a polynomial ring. (MATH 0200 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0302">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0402 - Topics In Algebra
</h5>
<div class='coursedesc'>
<p><strong>Topics in Algebra</strong><br />
A further study of topics from MATH 0302. These may include field theory, algebraic extension fields, Galois theory, solvability of polynomial equations by radicals, finite fields, elementary algebraic number theory, solution of the classic geometric construction problems, or the classical groups. (MATH 0302 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2012</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0402">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0500 - Advanced Study
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Advanced Study</strong><br />
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc. </p>
<p>Fall 2011, Winter 2012, Spring 2012, Winter 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Spring 2016</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0500">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0704 - Senior Seminar
</h5>
<div class='coursedesc'>
<p><strong>Senior Seminar</strong><br />
Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc. </p>
<p>Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0704">More Information »</a></p>
</div>
</div></div></div>Thu, 12 Nov 2009 17:05:00 +0000Naomi Neff nneff@middlebury.edu26431 at http://www.middlebury.eduSteve Abbott
http://www.middlebury.edu/academics/math/faculty/node/26391
<div class="field field-name-field-features field-type-list-text field-label-above"><div class="field-label">Dynamic Features: </div><div class="field-items"><div class="field-item even">Course Catalog</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Degrees, Specializations & Interests:</strong><br /><span>A.B., Colgate University; M.S., Ph.D., University of Virginia; (Functional Analysis, Operator Theory)</span></p>
<p><span>Awarded the 2010 Perkins Award for Excellence in Teaching, see story <a href="http://www.middlebury.edu/newsroom/node/252651" target="_blank">here</a>.<br /></span></p>
<p><span><a href="http://community.middlebury.edu/~abbott/">Personal Homepage</a><br /></span></p></div></div></div><div class="field field-name-field-extras field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><h4>Co-Editor <em>Math Horizons</em></h4>
<p> </p>
<div>
<div><a href="http://www.maa.org/mathhorizons/"><span><img src="/media/view/222961/thumbnail/MHorizonsNov2009.jpg" alt="Math Horizons November Cover" title="Math Horizons November Cover" width="116" height="150" style="border:0pt none; margin:10px; float:left" /></span></a></div>
</div>
<p>Of all of the publications we know <em>Math Horizons</em> is the broadest, most creative forum that exists for communicating the culture, characters and folklore of mathematics today's students. Whether helping our students to know and care about the "who" and the "why" of their chosen subject, giving voice to its current practitioners, or shedding light on the interface between mathematics and the larger academic or popular culture, <em>Math Horizons </em>always explores its subjects with an inviting tone and trademark accessibility.</p>
<p>For going on fifteen years, <em>Math Horizons</em> has exposed undergraduates-and instructors-to the mathematical world beyond the classroom with authentic detail and good humor that make it easy to pick up and irresistible to read.</p>
<p><strong>Bruce Torrence and Steve Abbott; Co-Editors, <em>Math Horizons</em></strong></p>
<p> </p></div></div></div><div class="field field-name-field-user field-type-user-reference field-label-above"><div class="field-label">User: </div><div class="field-items"><div class="field-item even"><a href="/user/12311">Stephen Abbott abbott@middlebury.edu</a></div></div></div><div class="field field-name-field-feeditems field-type-list-integer field-label-above"><div class="field-label">Items per Feed: </div><div class="field-items"><div class="field-item even">2</div></div></div><div class="field field-name-middlebury-course-list field-type-middlebury-course-list-courses field-label-above"><div class="field-label">Course List: </div><div class="field-items"><div class="field-item even">
<p>Courses offered in the past four years. <br/><span title="Offered in the current term">▲</span> <em>indicates offered in the current term</em><br/><span title="Offered in the upcoming term[s]">▹</span> <em>indicates offered in the upcoming term[s]</em></p>
<h5 class='coursetitle'>FYSE 1211 - Godel, Escher, Bach
</h5>
<div class='coursedesc'>
<p><strong>Gödel, Escher, Bach</strong><br />
At the turn of the 20th century, mathematics took an introspective turn when its practitioners attempted to organize reasoning itself into an axiomatic system of theorems and definitions. The results were provocative and ended in a kind of paradox when logician Kurt Gödel proved that all formalized logical systems would necessarily contain some unprovable truths. Reading Douglas Hofstadter's <em>Gödel, Escher, Bach</em>, we will discover the connections among seemingly disparate fields of mathematics, visual arts, and music. Our journey will pass through the philosophical worlds of Lewis Carroll, Artificial Intelligence, non-Euclidean geometry, Zen Buddhism, and crash head-on into questions about the nature of human consciousness and creativity. 3 hrs. sem. <strong>CW DED</strong>
</p>
<p>Spring 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FFYSE1211">More Information »</a></p>
</div>
<h5 class='coursetitle'>INTD 0206 - Math/Science Contemp. Theatre
</h5>
<div class='coursedesc'>
<p><strong>Mathematics and Science as Art in Contemporary Theatre</strong><br />
In Tom Stoppard’s Jumpers, philosopher George Moore employs a list of mathematical arguments to make his case for the existence of a moral God. George’s confused allusions to the paradoxes of Zeno and Bertrand Russell form an interesting backdrop to a host of moral questions that include an astronaut stranded on the moon, the installation of an atheist as Archbishop of Canterbury and the mysterious circumstances surrounding the dead body of George’s debating partner concealed in the next room. This is just one example of how acclaimed playwrights such as Tom Stoppard, Rinne Groff, Michael Frayn, and others have effectively explored mathematical and scientific themes for artistic purposes. Through readings and exercises, and by conducting labs and staging scenes, this class will gain some first-hand insight into the complementary ways in which science and art aim to seek out their respective truths. <strong>DED LIT</strong>
</p>
<p>Fall 2011, Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FINTD0206">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0121 - Calculus I
</h5>
<div class='coursedesc'>
<p><strong>Calculus I</strong><br />
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2012, Spring 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0121">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0122 - Calculus II
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Calculus II</strong><br />
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2011, Fall 2013, Fall 2014, Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0122">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0200 - Linear Algebra
</h5>
<div class='coursedesc'>
<p><strong>Linear Algebra</strong><br />
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2012, Spring 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0200">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0323 - Real Analysis
</h5>
<div class='coursedesc'>
<p><strong>Real Analysis</strong><br />
An axiomatic treatment of the topology of the real line, real analysis, and calculus. Topics include neighborhoods, compactness, limits, continuity, differentiation, Riemann integration, and uniform convergence. (MATH 0223) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2012, Spring 2014, Fall 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0323">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0423 - Topics in Analysis
</h5>
<div class='coursedesc'>
<p><strong>Topics in Analysis</strong><br />
In this course we will study advanced topics in real analysis, starting from the fundamentals established in MA401. Topics may include: basic measure theory; Lebesgue measure on Euclidean space; the Lebesgue integral; total variation and absolute continuity; basic functional analysis; fractal measures. (MATH 0323 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0423">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0500 - Advanced Study
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Advanced Study</strong><br />
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc. </p>
<p>Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Spring 2016</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0500">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0704 - Senior Seminar
</h5>
<div class='coursedesc'>
<p><strong>Senior Seminar</strong><br />
Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc. </p>
<p>Spring 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0704">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 1006 - Heart of Mathematics
</h5>
<div class='coursedesc'>
<p><strong>The Heart of Mathematics</strong><br />
Wrestling with the infinite, tiling a floor, predicting the shape of space, imagining the fourth dimension, untangling knots, making pictures of chaos, conducting an election, cutting a cake fairly; all of these topics are part of the landscape of mathematics, although they are largely excluded from the calculus-centric way that the subject is traditionally presented. Following the acclaimed text, <em>The Heart of Mathematics</em>, by Ed Burger and Michael Starbird, we will dive headfirst into ideas that reveal the beauty and diverse character of pure mathematics, employing effective modes of reasoning that are useful far beyond the boundaries of the discipline. <strong>DED WTR</strong>
</p>
<p>Winter 2012</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH1006">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 1015 / PHIL 1015 - Philosophy of Mathematics
</h5>
<div class='coursedesc'>
<p><strong>Philosophy of Mathematics</strong><br />
Mathematics is one of humankind’s greatest cognitive endeavors, yet it raises many puzzling questions. Unlike much of our other knowledge, most mathematical knowledge is not established by gathering empirical evidence. So how is mathematical knowledge possible? Unlike most other things we consider to be real, mathematical objects are not physical objects. So in what sense do mathematical objects, such as numbers, exist? What are the foundations of mathematics? Do some mathematical proofs provide greater understanding than others? No prior knowledge of mathematics or philosophy is required. <strong>DED PHL WTR</strong>
</p>
<p>Winter 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH1015">More Information »</a></p>
</div>
</div></div></div>Thu, 12 Nov 2009 16:56:00 +0000Naomi Neff nneff@middlebury.edu26391 at http://www.middlebury.eduDavid Dorman
http://www.middlebury.edu/academics/math/faculty/node/26441
<div class="field field-name-field-features field-type-list-text field-label-above"><div class="field-label">Dynamic Features: </div><div class="field-items"><div class="field-item even">Course Catalog</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Degrees, Specializations & Interests:</strong><br /><span>B.S., Hobart College; Sc.M., Ph.D., Brown University; <br />(Number Theory, Algebraic Geometry)</span></p>
<p><span><a href="http://community.middlebury.edu/~dorman/" target="_blank">homepage</a><br /></span></p></div></div></div><div class="field field-name-field-user field-type-user-reference field-label-above"><div class="field-label">User: </div><div class="field-items"><div class="field-item even"><a href="/user/10846">David Dorman dorman@middlebury.edu</a></div></div></div><div class="field field-name-field-feeditems field-type-list-integer field-label-above"><div class="field-label">Items per Feed: </div><div class="field-items"><div class="field-item even">2</div></div></div><div class="field field-name-middlebury-course-list field-type-middlebury-course-list-courses field-label-above"><div class="field-label">Course List: </div><div class="field-items"><div class="field-item even">
<p>Courses offered in the past four years. <br/><span title="Offered in the current term">▲</span> <em>indicates offered in the current term</em><br/><span title="Offered in the upcoming term[s]">▹</span> <em>indicates offered in the upcoming term[s]</em></p>
<h5 class='coursetitle'>FYSE 1346 - Math Models Bio & Epidemiology
</h5>
<div class='coursedesc'>
<p><strong>Mathematical Modeling in Biology and Epidemiology</strong><br />
Population growth, species interactions, and the transmission and treatment of infectious diseases have long been central foci in biology. Mathematical modeling has tremendously influenced the ongoing research in these areas and has greatly contributed to our understanding. In this course we will investigate a variety of discrete and continuous mathematical models used in these areas. We will explore original research and will learn how to critique existing models. We will formulate and investigate our own questions by building, analyzing, and testing new models. (Calculus) 3 hrs. sem. <strong>CW DED</strong>
</p>
<p>Fall 2011</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FFYSE1346">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0121 - Calculus I
</h5>
<div class='coursedesc'>
<p><strong>Calculus I</strong><br />
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0121">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0122 - Calculus II
</h5>
<div class='coursedesc'>
<p><strong>Calculus II</strong><br />
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2014, Spring 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0122">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0200 - Linear Algebra
</h5>
<div class='coursedesc'>
<p><strong>Linear Algebra</strong><br />
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2012, Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0200">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0217 - Elements of Math Bio & Ecol
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Elements of Mathematical Biology and Ecology</strong><br />
Mathematical modeling has become an essential tool in biology and ecology. In this course we will investigate several fundamental biological and ecological models. We will learn how to analyze existing models and how to construct new models. We will develop ecological and evolutionary models that describe how biological systems change over time. Models for population growth, predator-prey interactions, competing species, the spread of infectious disease, and molecular evolution will be studied. Students will be introduced to differential and difference equations, multivariable calculus, and linear and non-linear dynamical systems. (MATH 0121 or by waiver) <strong>DED</strong>
</p>
<p>Fall 2013, Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0217">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0223 - Multivariable Calculus
</h5>
<div class='coursedesc'>
<p><strong>Multivariable Calculus</strong><br />
The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. (MATH 0122 and MATH 0200 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2011, Spring 2012</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0223">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0225 - Topics in Linear Alg & Diff Eq
</h5>
<div class='coursedesc'>
<p><strong>Topics in Linear Algebra and Differential Equations</strong><br />
Topics may include diagonalization of matrices, quadratic forms, inner product spaces, canonical forms, the spectral theorem, positive matrices, the Cayley-Hamilton theorem, ordinary differential equations of arbitrary order, systems of first-order differential equations, power series, and eigenvalue methods of solution, applications. (MATH 0200 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2012, Spring 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0225">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0241 - Elementary Number Theory
</h5>
<div class='coursedesc'>
<p><strong>Elementary Number Theory</strong><br />
Divisibility and prime factorization. Congruences; the theorems of Lagrange, Fermat, Wilson, and Euler; residue theory; quadratic reciprocity. Diophantine equations. Arithmetic functions and Mobius inversion. Representation as a sum of squares. (MATH 0122 or by waiver) <strong>DED</strong>
</p>
<p>Spring 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0241">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0302 - Abstract Algebra I
</h5>
<div class='coursedesc'>
<p><strong>Abstract Algebra</strong><br />
Groups, subgroups, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, rings and ideals, integral domains and fields, the field of quotients of a domain, the ring of polynomials over a domain, Euclidean domains, principal ideal domains, unique factorization, factorization in a polynomial ring. (MATH 0200 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2012</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0302">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0500 - Advanced Study
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Advanced Study</strong><br />
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc. </p>
<p>Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Spring 2016</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0500">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0702 - Senior Seminar
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Advanced Algebra and Number Theory Seminar</strong><br />
This course is a tutorial in Advanced Abstract Algebra and Number Theory for students who have completed work in either subject. Starting from elementary results in linear algebra, we will explore the fundamental mathematical ideas underlying field extensions, constructability, unique factorization, Euclidean fields, and Galois theory. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0241 or MATH 0302; Approval required) 3 hrs. sem. </p>
<p>Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0702">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0704 - Senior Seminar
</h5>
<div class='coursedesc'>
<p><strong>Senior Seminar</strong><br />
Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc. </p>
<p>Fall 2011, Spring 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0704">More Information »</a></p>
</div>
</div></div></div>Thu, 12 Nov 2009 17:07:00 +0000Naomi Neff nneff@middlebury.edu26441 at http://www.middlebury.eduJohn Emerson
http://www.middlebury.edu/academics/math/faculty/node/26451
<div class="field field-name-field-features field-type-list-text field-label-above"><div class="field-label">Dynamic Features: </div><div class="field-items"><div class="field-item even">Course Catalog</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Degrees, Specializations & Interests:</strong><br /><span>A.B., University of Rochester; M.S., Ph.D., Cornell University; (Statistical methods, Data Analysis, Biostatistics)</span></p></div></div></div><div class="field field-name-field-extras field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><h4>Recent Publications</h4>
<p>Moses, L.E., Emerson, J.D., and Hosseini, H. "Analyzing Data from Ordered Categories." In J.C. Bailar III and D. Hoaglin, Eds., <em>Medical Uses of Statistics</em>,<em> 3rd Ed.,</em> Hoboken, NJ: Wiley. 2009, 311-323.</p>
<p>Agarwal, S., Colditz, G.A., and Emerson, J.D. "Use of Statistical Analysis in the New England Journal of Medicine." In J.C. Bailar III and D. Hoaglin, Eds., <em>Medical Uses of Statistics</em>, <em> 3rd Ed.,</em> Hoboken, NJ: Wiley. 2009, 41-49.</p>
<p>Emerson, J.D., Brooks, R.L., and McKenzie, E.C. "College Sports and Student Achievement: The Evidence at Small Colleges." In <em>Data-Driven Decision-Making in Intercollegiate Athletics. </em>New Directions in Institutional Research, edited by J.L. Hoffman, J.S. Antony, and D.D. Alfaro. San Francisco: Jossey-Bass, No. 144, 2009, 65-76.</p></div></div></div><div class="field field-name-field-user field-type-user-reference field-label-above"><div class="field-label">User: </div><div class="field-items"><div class="field-item even"><a href="/user/8487">John Emerson jemerson@middlebury.edu</a></div></div></div><div class="field field-name-field-feeditems field-type-list-integer field-label-above"><div class="field-label">Items per Feed: </div><div class="field-items"><div class="field-item even">2</div></div></div><div class="field field-name-middlebury-course-list field-type-middlebury-course-list-courses field-label-above"><div class="field-label">Course List: </div><div class="field-items"><div class="field-item even">
<p>Courses offered in the past four years. <br/><span title="Offered in the current term">▲</span> <em>indicates offered in the current term</em><br/><span title="Offered in the upcoming term[s]">▹</span> <em>indicates offered in the upcoming term[s]</em></p>
<h5 class='coursetitle'>MATH 0116 - Intro to Statistical Science
</h5>
<div class='coursedesc'>
<p><strong>Introduction to Statistical Science</strong><br />
A practical introduction to statistical methods and the examination of data sets. Computer software will play a central role in analyzing a variety of real data sets from the natural and social sciences. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, correlation, regression, contingency tables, and analysis of variance. The course has no formal mathematics prerequisite, and is especially suited to students in the physical, social, environmental, and life sciences who seek an applied orientation to data analysis. (Credit is not given for MATH 0116 if the student has taken ECON 0210 or PSYC 0201 previously or concurrently.) 3 hrs. lect./1 hr. computer lab. <strong>DED</strong>
</p>
<p>Fall 2012, Spring 2013, Spring 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0116">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0121 - Calculus I
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Calculus I</strong><br />
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0121">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0122 - Calculus II
</h5>
<div class='coursedesc'>
<p><strong>Calculus II</strong><br />
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2011, Spring 2012, Fall 2012, Spring 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0122">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0200 - Linear Algebra
</h5>
<div class='coursedesc'>
<p><strong>Linear Algebra</strong><br />
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2013, Spring 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0200">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0310 - Probability
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Probability</strong><br />
An introduction to the concepts of probability and their applications, covering both discrete and continuous random variables. Probability spaces, elementary combinatorial analysis, densities and distributions, conditional probabilities, independence, expectation, variance, weak law of large numbers, central limit theorem, and numerous applications. (concurrent or prior MATH 0223 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2011, Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0310">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0311 - Statistics
</h5>
<div class='coursedesc'>
<p><strong>Statistics</strong><br />
An introduction to the mathematical methods and applications of statistical inference. Topics will include: survey sampling, parametric and nonparametric problems, estimation, efficiency and the Neyman-Pearsons lemma. Classical tests within the normal theory such as F-test, t-test, and chi-square test will also be considered. Methods of linear least squares are used for the study of analysis of variance and regression. There will be some emphasis on applications to other disciplines. (MATH 0310) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2012, Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0311">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0500 - Advanced Study
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Advanced Study</strong><br />
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc. </p>
<p>Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Spring 2016</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0500">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 1139 / INTD 1139 - Statistics with Randomization
</h5>
<div class='coursedesc'>
<p><strong>Understanding Uncertainty: Exploring Data Using Randomization</strong><br />
In this course we will use computer-intensive methods to explore the randomness inherent in a data set and to develop the scientific logic of statistical inference. We will introduce randomization methods as a basis for framing fundamental concepts of inference: estimates, confidence intervals, and hypothesis tests. The capabilities of computers to draw thousands of random samples and to simulate experiments will replace theoretical approximations grounded in mathematical statistics, especially the normal theory methods like t-tests and chi-squared analyses. Students will use the R programming language to implement the analyses. Much of the course development will proceed through independent and collaborative computer investigations by students using real data sets. No prior experience with statistics and with computer programming is necessary. <strong>CW DED WTR</strong>
</p>
<p>Winter 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH1139">More Information »</a></p>
</div>
</div></div></div>Thu, 12 Nov 2009 17:08:00 +0000Naomi Neff nneff@middlebury.edu26451 at http://www.middlebury.eduMichaela Kubacki
http://www.middlebury.edu/academics/math/faculty/node/479588
<div class="field field-name-field-features field-type-list-text field-label-above"><div class="field-label">Dynamic Features: </div><div class="field-items"><div class="field-item even">Course Catalog</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Degrees, Specializations & Interests:</strong></p>
<p>B.A., Washington & Jefferson College; M.A., University of Pittsburgh; Ph.D., University of Pittsburgh;<br />(Numerical Analysis, Computational Fluid Dynamics)</p>
<p> </p></div></div></div><div class="field field-name-field-extras field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><h4></h4></div></div></div><div class="field field-name-field-user field-type-user-reference field-label-above"><div class="field-label">User: </div><div class="field-items"><div class="field-item even"><a href="/user/56956">Michaela Kubacki mkubacki@middlebury.edu</a></div></div></div><div class="field field-name-field-feeditems field-type-list-integer field-label-above"><div class="field-label">Items per Feed: </div><div class="field-items"><div class="field-item even">2</div></div></div><div class="field field-name-middlebury-course-list field-type-middlebury-course-list-courses field-label-above"><div class="field-label">Course List: </div><div class="field-items"><div class="field-item even">
<p>Courses offered in the past four years. <br/><span title="Offered in the current term">▲</span> <em>indicates offered in the current term</em><br/><span title="Offered in the upcoming term[s]">▹</span> <em>indicates offered in the upcoming term[s]</em></p>
<h5 class='coursetitle'>MATH 0122 - Calculus II
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Calculus II</strong><br />
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2014, Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0122">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0225 - Topics in Linear Alg & Diff Eq
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Topics in Linear Algebra and Differential Equations</strong><br />
Topics may include diagonalization of matrices, quadratic forms, inner product spaces, canonical forms, the spectral theorem, positive matrices, the Cayley-Hamilton theorem, ordinary differential equations of arbitrary order, systems of first-order differential equations, power series, and eigenvalue methods of solution, applications. (MATH 0200 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2014, Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0225">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0228 - Intro to Numerical Analysis
</h5>
<div class='coursedesc'>
<p><strong>Introduction to Numerical Analysis</strong><br />
We will study the development, analysis, and implementation of numerical methods for approximating solutions to mathematical problems. We will begin with applications of Taylor polynomials, computer representation of numbers, and types of errors. Other topics will include polynomial and spline interpolation, numerical integration and differentiation, rootfinding, and numerical solutions of differential equations. Accuracy will be quantified by the concept of numerical error. Additionally, we will study the stability, efficiency, and implementation of algorithms. We will utilize the software MATLAB throughout to demonstrate concepts, as well as to complete assignments and projects. (MATH 0200) <strong>DED</strong>
</p>
<p>Spring 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0228">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0500 - Advanced Study
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Advanced Study</strong><br />
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc. </p>
<p>Fall 2014, Winter 2015, Spring 2015, Fall 2015, Spring 2016</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0500">More Information »</a></p>
</div>
</div></div></div>Wed, 16 Jul 2014 17:46:24 +0000Naomi Neff nneff@middlebury.edu479588 at http://www.middlebury.eduhttp://www.middlebury.edu/academics/math/faculty/node/479588#commentsMichael Olinick
http://www.middlebury.edu/academics/math/faculty/node/26501
<div class="field field-name-field-features field-type-list-text field-label-above"><div class="field-label">Dynamic Features: </div><div class="field-items"><div class="field-item even">Course Catalog</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Degrees, Specializations & Interests:</strong><br /><span>A.B., University of Michigan; M.A., Ph.D., University of Wisconsin;</span></p>
<p><a href="http://community.middlebury.edu/~molinick/">Home Page</a></p></div></div></div><div class="field field-name-field-user field-type-user-reference field-label-above"><div class="field-label">User: </div><div class="field-items"><div class="field-item even"><a href="/user/11863">Michael Olinick molinick@middlebury.edu</a></div></div></div><div class="field field-name-field-feeditems field-type-list-integer field-label-above"><div class="field-label">Items per Feed: </div><div class="field-items"><div class="field-item even">2</div></div></div><div class="field field-name-middlebury-course-list field-type-middlebury-course-list-courses field-label-above"><div class="field-label">Course List: </div><div class="field-items"><div class="field-item even">
<p>Courses offered in the past four years. <br/><span title="Offered in the current term">▲</span> <em>indicates offered in the current term</em><br/><span title="Offered in the upcoming term[s]">▹</span> <em>indicates offered in the upcoming term[s]</em></p>
<h5 class='coursetitle'>FYSE 1280 / INTD 1065 - Breaking the Code: Alan Turing
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Breaking the Code: The Enigma of Alan Turing</strong><br />
British mathematician Alan Turing broke the Nazis' prized Enigma cipher in World War II, created the foundations of computer science, and pioneered the fields of artificial intelligence (“Can Machines Think?”) and neural networks. Turing was arrested for homosexuality and forced to undergo hormone treatments. He died by cyanide poisoning at a relatively young age. His brilliant achievements and tragic death have been the subject of biographies, essays, plays, novels, and films, most recently the Academy Award winning The Imitation Game. We will explore the life and works of this remarkable individual in the context of the war and its aftermath. 3 hrs. sem./screening <strong>CW DED EUR</strong>
</p>
<p>Winter 2012, Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FFYSE1280">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0121 - Calculus I
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Calculus I</strong><br />
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0121">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0122 - Calculus II
</h5>
<div class='coursedesc'>
<p><strong>Calculus II</strong><br />
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2012</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0122">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0200 - Linear Algebra
</h5>
<div class='coursedesc'>
<p><strong>Linear Algebra</strong><br />
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2012, Spring 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0200">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0223 - Multivariable Calculus
</h5>
<div class='coursedesc'>
<p><strong>Multivariable Calculus</strong><br />
The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. (MATH 0122 and MATH 0200 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0223">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0225 - Topics in Linear Alg & Diff Eq
</h5>
<div class='coursedesc'>
<p><strong>Topics in Linear Algebra and Differential Equations</strong><br />
Topics may include diagonalization of matrices, quadratic forms, inner product spaces, canonical forms, the spectral theorem, positive matrices, the Cayley-Hamilton theorem, ordinary differential equations of arbitrary order, systems of first-order differential equations, power series, and eigenvalue methods of solution, applications. (MATH 0200 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0225">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0315 - Mathematical Models
</h5>
<div class='coursedesc'>
<p><strong>Mathematical Models in the Social and Life Sciences</strong><br />
An introduction to the role of mathematics as a modeling tool and an examination of some mathematical models of proven usefulness in problems arising in the social and life sciences. Topics will be selected from the following: axiom systems as used in model building, optimization techniques, linear and integer programming, theory of games, systems of differential equations, computer simulation, stochastic process. Specific models in political science, ecology, sociology, anthropology, psychology, and economics will be explored. (MATH 0200 or waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0315">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0318 - Operations Research
</h5>
<div class='coursedesc'>
<p><strong>Operations Research</strong><br />
Operations research is the utilization of quantitative methods as an aid to managerial decisions. In the course, several of these methods will be introduced and studied in both a mathematical context and a physical context. Topics included will be selected from the following: classification of problems and the formulation of models, linear programming, network optimization, transportation problems, assignment problems, integer programming, nonlinear programming, inventory theory, and game theory. (MATH 0200 or waiver) <strong>DED</strong>
</p>
<p>Spring 2012, Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0318">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0323 - Real Analysis
</h5>
<div class='coursedesc'>
<p><strong>Real Analysis</strong><br />
An axiomatic treatment of the topology of the real line, real analysis, and calculus. Topics include neighborhoods, compactness, limits, continuity, differentiation, Riemann integration, and uniform convergence. (MATH 0223) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2011, Spring 2012</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0323">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0432 - Elementary Topology
</h5>
<div class='coursedesc'>
<p><strong>Elementary Topology</strong><br />
An introduction to the concepts of topology. Theory of sets, general topological spaces, topology of the real line, continuous functions and homomorphisms, compactness, connectedness, metric spaces, selected topics from the topology of Euclidean spaces including the Jordan curve theorem. (MATH 0122 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0432">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0500 - Advanced Study
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Advanced Study</strong><br />
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc. </p>
<p>Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0500">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0704 - Senior Seminar
</h5>
<div class='coursedesc'>
<p><strong>Senior Seminar</strong><br />
Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc. </p>
<p>Spring 2012</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0704">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 1009 / FYSE 1229 - Discovering Infinity
</h5>
<div class='coursedesc'>
<p><strong>Discovering Infinity</strong> <br />
"Infinity" has intrigued poets, artists, philosophers, musicians, religious thinkers, physicists, astronomers, and mathematicians throughout the ages. Beginning with puzzles and paradoxes that show the need for careful definition and rigorous thinking, we will examine the idea of infinity within mathematics, discovering and presenting our own theorems and proofs about the infinite. Our central focus will be the evolution of the mathematician’s approach to infinity, for it is here that the concept has its deepest roots and where our greatest understanding lies. In the final portion of the course, we will consider representation of the infinite in literature and the arts. (Not open to students who have taken FYSE 1229). 3 hrs. lect. <strong>DED PHL WTR</strong>
</p>
<p>Fall 2011, Winter 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH1009">More Information »</a></p>
</div>
</div></div></div>Thu, 12 Nov 2009 18:12:00 +0000Naomi Neff nneff@middlebury.edu26501 at http://www.middlebury.eduBruce Peterson
http://www.middlebury.edu/academics/math/faculty/node/26521
<div class="field field-name-field-features field-type-list-text field-label-above"><div class="field-label">Dynamic Features: </div><div class="field-items"><div class="field-item even">Course Catalog</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"></div></div></div><div class="field field-name-field-user field-type-user-reference field-label-above"><div class="field-label">User: </div><div class="field-items"><div class="field-item even"><a href="/user/10816">Bruce Peterson peterson@middlebury.edu</a></div></div></div><div class="field field-name-field-feeditems field-type-list-integer field-label-above"><div class="field-label">Items per Feed: </div><div class="field-items"><div class="field-item even">2</div></div></div><div class="field field-name-middlebury-course-list field-type-middlebury-course-list-courses field-label-above"><div class="field-label">Course List: </div><div class="field-items"><div class="field-item even">
<p>Courses offered in the past four years. <br/><span title="Offered in the current term">▲</span> <em>indicates offered in the current term</em><br/><span title="Offered in the upcoming term[s]">▹</span> <em>indicates offered in the upcoming term[s]</em></p>
<h5 class='coursetitle'>CSCI 0200 - Math Foundations of Computing
</h5>
<div class='coursedesc'>
<p><strong>Mathematical Foundations of Computing</strong><br />
In this course we will provide an introduction to the mathematical foundations of computer science, with an emphasis on formal reasoning. Topics will include propositional and predicate logic, sets, functions, and relations; basic number theory; mathematical induction and other proof methods; combinatorics, probability, and recurrence relations; graph theory; and models of computation. (One CSCI course at the 0100-level previously or concurrently) 3 hrs. lect./lab <strong>DED</strong>
</p>
<p>Spring 2012</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FCSCI0200">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0121 - Calculus I
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Calculus I</strong><br />
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2011, Fall 2012, Spring 2014, Fall 2014, Spring 2015, Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0121">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0122 - Calculus II
</h5>
<div class='coursedesc'>
<p><strong>Calculus II</strong><br />
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0122">More Information »</a></p>
</div>
</div></div></div>Thu, 12 Nov 2009 17:14:00 +0000Naomi Neff nneff@middlebury.edu26521 at http://www.middlebury.eduWilliam Peterson
http://www.middlebury.edu/academics/math/faculty/node/26511
<div class="field field-name-field-features field-type-list-text field-label-above"><div class="field-label">Dynamic Features: </div><div class="field-items"><div class="field-item even">Course Catalog</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Degrees, Specializations & Interests:</strong><br /><span>A.B., Dartmouth College; M.S., Ph.D., Stanford University;<br /><br />Applied Probability, Stochastic Processes</span></p>
<p><span><a href="http://community.middlebury.edu/~wpeterso/">Website</a><br /></span></p></div></div></div><div class="field field-name-field-extras field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><h4>Math 116</h4>
<p>webpage</p></div></div></div><div class="field field-name-field-user field-type-user-reference field-label-above"><div class="field-label">User: </div><div class="field-items"><div class="field-item even"><a href="/user/23281">William Peterson wpeterso@middlebury.edu</a></div></div></div><div class="field field-name-field-feeditems field-type-list-integer field-label-above"><div class="field-label">Items per Feed: </div><div class="field-items"><div class="field-item even">2</div></div></div><div class="field field-name-middlebury-course-list field-type-middlebury-course-list-courses field-label-above"><div class="field-label">Course List: </div><div class="field-items"><div class="field-item even">
<p>Courses offered in the past four years. <br/><span title="Offered in the current term">▲</span> <em>indicates offered in the current term</em><br/><span title="Offered in the upcoming term[s]">▹</span> <em>indicates offered in the upcoming term[s]</em></p>
<h5 class='coursetitle'>FYSE 1025 - Chance
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Chance *<br />
A prominent statistician once wrote, “Statistics exists only at the interfaces of chance and empirical data. But it exists at every such interface.” Are most cancers attributable to bad luck, as Forbes recently suggested? Do fluctuations in US News college rankings reflect educational quality? Is texting while driving riskier than drunk driving? You can't follow the news, choose a college, or even get behind the wheel without encountering statistical claims. Which should you trust? Our readings will include your favorite newspaper, Stephen J. Gould's essays on excellence and variability, and Edward Tufte's critique of data graphics in the popular press.. 3 hrs. sem.</strong> <strong>CW DED</strong>
</p>
<p>Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FFYSE1025">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0116 - Intro to Statistical Science
</h5>
<div class='coursedesc'>
<p><strong>Introduction to Statistical Science</strong><br />
A practical introduction to statistical methods and the examination of data sets. Computer software will play a central role in analyzing a variety of real data sets from the natural and social sciences. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, correlation, regression, contingency tables, and analysis of variance. The course has no formal mathematics prerequisite, and is especially suited to students in the physical, social, environmental, and life sciences who seek an applied orientation to data analysis. (Credit is not given for MATH 0116 if the student has taken ECON 0210 or PSYC 0201 previously or concurrently.) 3 hrs. lect./1 hr. computer lab. <strong>DED</strong>
</p>
<p>Fall 2011, Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0116">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0121 - Calculus I
</h5>
<div class='coursedesc'>
<p><strong>Calculus I</strong><br />
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2012, Spring 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0121">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0122 - Calculus II
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Calculus II</strong><br />
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2014, Fall 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0122">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0200 - Linear Algebra
</h5>
<div class='coursedesc'>
<p><strong>Linear Algebra</strong><br />
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0200">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0310 - Probability
</h5>
<div class='coursedesc'>
<p><strong>Probability</strong><br />
An introduction to the concepts of probability and their applications, covering both discrete and continuous random variables. Probability spaces, elementary combinatorial analysis, densities and distributions, conditional probabilities, independence, expectation, variance, weak law of large numbers, central limit theorem, and numerous applications. (concurrent or prior MATH 0223 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2012, Spring 2014, Fall 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0310">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0410 - Stochastic Processes
</h5>
<div class='coursedesc'>
<p><strong>Stochastic Processes</strong><br />
Stochastic processes are mathematical models for random phenomena evolving in time or space. This course will introduce important examples of such models, including random walk, branching processes, the Poisson process and Brownian motion. The theory of Markov chains in discrete and continuous time will be developed as a unifying theme. Depending on time available and interests of the class, applications will be selected from the following areas: queuing systems, mathematical finance (Black-Scholes options pricing), probabilistic algorithms, and Monte Carlo simulation. (MATH 0310) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2013, Spring 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0410">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0500 - Advanced Study
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Advanced Study</strong><br />
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc. </p>
<p>Fall 2011, Winter 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Spring 2016</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0500">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0710 - Advanced Probablility Seminar
</h5>
<div class='coursedesc'>
<p><strong>Advanced Probability Seminar</strong><br />
This course is a tutorial in Probability Theory for students who have completed work in Probability and Real Analysis. Starting from elementary results about random walks, we will explore the fundamental mathematical ideas underlying measure theoretic probability, martingales, the Weiner process, and the Itô stochastic calculus. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0310, MATH 0323, and by approval). 3 hrs. sem. </p>
<p>Fall 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0710">More Information »</a></p>
</div>
</div></div></div>Thu, 12 Nov 2009 17:13:00 +0000Naomi Neff nneff@middlebury.edu26511 at http://www.middlebury.eduEmily Proctor
http://www.middlebury.edu/academics/math/faculty/node/26541
<div class="field field-name-field-features field-type-list-text field-label-above"><div class="field-label">Dynamic Features: </div><div class="field-items"><div class="field-item even">Course Catalog</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Degrees, Specializations & Interests:</strong><br /><span>A.M. , Bowdoin College; A.M., Ph.D. Dartmouth College;<br />(Riemannian Geometry)</span></p>
<p><a href="http://community.middlebury.edu/~eproctor/">Website</a></p></div></div></div><div class="field field-name-field-user field-type-user-reference field-label-above"><div class="field-label">User: </div><div class="field-items"><div class="field-item even"><a href="/user/2329">Emily Proctor eproctor@middlebury.edu</a></div></div></div><div class="field field-name-field-feeditems field-type-list-integer field-label-above"><div class="field-label">Items per Feed: </div><div class="field-items"><div class="field-item even">2</div></div></div><div class="field field-name-middlebury-course-list field-type-middlebury-course-list-courses field-label-above"><div class="field-label">Course List: </div><div class="field-items"><div class="field-item even">
<p>Courses offered in the past four years. <br/><span title="Offered in the current term">▲</span> <em>indicates offered in the current term</em><br/><span title="Offered in the upcoming term[s]">▹</span> <em>indicates offered in the upcoming term[s]</em></p>
<h5 class='coursetitle'>FYSE 1423 - The Story of Geometry
</h5>
<div class='coursedesc'>
<p><strong>The Story of Geometry</strong><br />
The field of geometry is thousands of years old and over time has undergone a number of revolutionary changes. In this seminar we will study geometry through a historical lens. Beginning with the axiomatic geometry of Euclid, we will trace the development of the subject, learning how the realization in the mid-19th century that one of Euclid’s axioms could be dropped led to the exciting discovery of hyperbolic and spherical geometries. We will learn how these geometries relate to the modern notions of manifolds and curvature, concluding with a discussion of Perelman’s breakthrough proof of the century-old Poincaré Conjecture. 3 hrs. sem. <strong>CW DED</strong>
</p>
<p>Fall 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FFYSE1423">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0121 - Calculus I
</h5>
<div class='coursedesc'>
<p><strong>Calculus I</strong><br />
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2011, Spring 2012, Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0121">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0223 - Multivariable Calculus
</h5>
<div class='coursedesc'>
<p><strong>Multivariable Calculus</strong><br />
The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. (MATH 0122 and MATH 0200 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2012, Spring 2014, Spring 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0223">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0302 - Abstract Algebra I
</h5>
<div class='coursedesc'>
<p><strong>Abstract Algebra</strong><br />
Groups, subgroups, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, rings and ideals, integral domains and fields, the field of quotients of a domain, the ring of polynomials over a domain, Euclidean domains, principal ideal domains, unique factorization, factorization in a polynomial ring. (MATH 0200 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2011, Spring 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0302">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0323 - Real Analysis
</h5>
<div class='coursedesc'>
<p><strong>Real Analysis</strong><br />
An axiomatic treatment of the topology of the real line, real analysis, and calculus. Topics include neighborhoods, compactness, limits, continuity, differentiation, Riemann integration, and uniform convergence. (MATH 0223) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0323">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0335 - Differential Geometry
</h5>
<div class='coursedesc'>
<p><strong>Differential Geometry</strong><br />
This course will be an introduction to the concepts of differential geometry. For curves in space, we will discuss arclength parameterizations, Frenet formulas, curvature, and torsion. On surfaces, we will explore the Gauss map, the shape operator, and various types of curvature. We will apply our knowledge to understand geodesics, metrics, and isometries of general geometric spaces. If time permits, we will consider topics such as minimal surfaces, constant curvature spaces, and the Gauss-Bonnet theorem. (MATH 0200 and MATH 0223) 3 hr. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2013, Fall 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0335">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0402 - Topics In Algebra
</h5>
<div class='coursedesc'>
<p><strong>Topics in Algebra</strong><br />
A further study of topics from MATH 0302. These may include field theory, algebraic extension fields, Galois theory, solvability of polynomial equations by radicals, finite fields, elementary algebraic number theory, solution of the classic geometric construction problems, or the classical groups. (MATH 0302 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0402">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0500 - Advanced Study
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Advanced Study</strong><br />
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc. </p>
<p>Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Spring 2016</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0500">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0704 - Senior Seminar
</h5>
<div class='coursedesc'>
<p><strong>Senior Seminar</strong><br />
Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc. </p>
<p>Spring 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0704">More Information »</a></p>
</div>
</div></div></div>Thu, 12 Nov 2009 17:15:00 +0000Naomi Neff nneff@middlebury.edu26541 at http://www.middlebury.eduJohn Schmitt
http://www.middlebury.edu/academics/math/faculty/node/21051
<div class="field field-name-field-features field-type-list-text field-label-above"><div class="field-label">Dynamic Features: </div><div class="field-items"><div class="field-item even">Course Catalog</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p> </p>
<p>John Schmitt (<a href="http://community.middlebury.edu/~jschmitt/">homepage</a>) is an Associate Professor of Mathematics and has been at Middlebury College since 2005. He received his B.A. from Providence College, his M.S. from the University of Vermont, and a Ph.D. from Emory University. <br /><br />His research interests are in combinatorics (the art of counting) and graph theory. As such, he has co-authored over ten <a href="http://www.ams.org/mathscinet/search/publications.html?pg1=IID&s1=781655" target="_blank">research articles</a>, most dealing with extremal graph theory, and has a similar number of co-authors. His <a href="http://www.oakland.edu/enp/" target="_blank">Erdös number</a> is two. His research has been supported by the following external sources: National Science Foundation, National Security Agency and VT-EPSCoR. In addition to having given invited lectures at many universities, most recently he was a Visiting Fellow at the Institute for Pure and Applied Mathematics at UCLA.<br /><br />Professor Schmitt enjoys teaching students how to count and play (combinatorial) games – things they thought they already knew. Students are frequently involved with his research. His efforts in teaching were recognized by students in 2008 with the Perkins Award.<br /><br />Away from academic life, he enjoys spending time with his family in the great outdoors of Vermont.</p></div></div></div><div class="field field-name-field-alttitle field-type-text field-label-above"><div class="field-label">Alternate Job Title: </div><div class="field-items"><div class="field-item even">Associate Professor of Mathematics</div></div></div><div class="field field-name-field-title2 field-type-text field-label-hidden"><div class="field-items"><div class="field-item even">test</div></div></div><div class="field field-name-field-altemail field-type-text field-label-above"><div class="field-label">Alternate Email: </div><div class="field-items"><div class="field-item even">jschmitt@middlebury.edu</div></div></div><div class="field field-name-field-extras field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><h4>Publications</h4>
<p>M. Ferrara and J. Schmitt, <em>A General Lower Bound for Potentially H-Graphic Degree Sequences</em>, SIAM J. Discrete Math., 23 (2009) 1, 517-526.<br />M. Ferrara, M. Jacobson, J. Schmitt and M. Siggers, <em>Potentially H-Bigraphic Sequences</em>, to appear in Discuss. Math. Graph Theory<br />M. Ferrara, R Gould and J. Schmitt, <em>Using Edge Exchanges to Prove the Erdos-Jacobson-Lehel Conjecture</em>, Bull. Inst. Combin. Appl., 57 (2009), 73-80.<br />O. Pikhurko and J. Schmitt, <em>A Note on Minimum K2;3-saturated Graphs</em>, Austral. J. of Combin., 40 (2008), 211-215.<br />Guantao Chen, M. Ferrrara, R. Gould and J. Schmitt, <em>Graphic Sequences with a Realization Containing a Complete Multipartite Subgraph</em>, Discrete Math., 308 (2008) 23, 5712-5721.<br />J. Yin, Gang Chen and J. Schmitt, <em>Graphic Sequences with a Realization Containing a Generalized Friendship Graph</em>, Discrete Math., 308 (2008) 24, 6226-6232.<br />R. Gould and J. Schmitt, <em>Minimum Degree and the Minimum Size of K^t_2-saturated graphs</em>, Discrete Math., 307 (2007) 9-10, 1108-1114.<br />M. Ferrara, R. Gould and J. Schmitt, <em>Graphic Sequences with a Realization Containing a Friendship Graph</em>, Ars Combin., 85 (2007), 161-171.<br />R. Gould, T. Luczak and J. Schmitt, <em>A Constructive Upper Bound for Cycle Saturated Graphs of Minimum Size</em>, Electron. J. Combin., 13 (2006) R29, 19pp.</p>
<h4>Synergistic Activities</h4>
<p>Conference organizer of Discrete Mathematics Days of the Northeast in September 2007. This conference, sponsored by the National Security Agency and Middlebury College, brought together world-class mathematicians, researchers, and graduate and undergraduate students.</p>
<h4>Selected Invited and Sponsored Talks</h4>
<p>Dartmouth College Combinatorics Seminar, October 2008, "<em>A dual to the Turán problem</em>".<br />University of Vermont Mathematics Colloquium, April 2007, "<em>Extremal Problems on Bipartite Graphs</em>".<br />Horizons of Combinatorics, Lake Balaton, Hungary, July 2006, "<em>On a Relationship of Two Extremal Functions</em>". (Support from the European Mathematical Society.)<br />6th Czech-Slovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications, Prague, Czech Republic, July 2006, "<em>An Erdös-Stone Type Conjecture</em>". (Partial support from DIMATIA of Charles University.)</p>
<p> </p>
<p> </p></div></div></div><div class="field field-name-field-user field-type-user-reference field-label-above"><div class="field-label">User: </div><div class="field-items"><div class="field-item even"><a href="/user/2559">John Schmitt jschmitt@middlebury.edu</a></div></div></div><div class="field field-name-field-altphone field-type-text field-label-above"><div class="field-label">Alternate Phone: </div><div class="field-items"><div class="field-item even">802.443.5952</div></div></div><div class="field field-name-field-profile-photo field-type-mm-fields-mm-nodelist field-label-above"><div class="field-label">Alternate Photo: </div><div class="field-items"><div class="field-item even">directoryimage</div></div></div><div class="field field-name-field-feeditems field-type-list-integer field-label-above"><div class="field-label">Items per Feed: </div><div class="field-items"><div class="field-item even">2</div></div></div><div class="field field-name-middlebury-course-list field-type-middlebury-course-list-courses field-label-above"><div class="field-label">Course List: </div><div class="field-items"><div class="field-item even">
<p>Courses offered in the past four years. <br/><span title="Offered in the current term">▲</span> <em>indicates offered in the current term</em><br/><span title="Offered in the upcoming term[s]">▹</span> <em>indicates offered in the upcoming term[s]</em></p>
<h5 class='coursetitle'>MATH 0122 - Calculus II
</h5>
<div class='coursedesc'>
<p><strong>Calculus II</strong><br />
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. (MATH 0121 or by waiver) 4 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Spring 2012, Spring 2013, Fall 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0122">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0200 - Linear Algebra
</h5>
<div class='coursedesc'>
<p><strong>Linear Algebra</strong><br />
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2011, Spring 2013, Spring 2014, Fall 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0200">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0223 - Multivariable Calculus
</h5>
<div class='coursedesc'>
<p><strong>Multivariable Calculus</strong><br />
The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. (MATH 0122 and MATH 0200 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2012, Fall 2013, Fall 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0223">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0247 - Graph Theory
</h5>
<div class='coursedesc'>
<p><strong>Graph Theory</strong> <br />
A graph (or network) is a useful mathematical model when studying a set of discrete objects and the relationships among them. We often represent an object with a vertex (node) and a relation between a pair with an edge (line). With the graph in hand, we then ask questions, such as: Is it connected? Can one traverse each edge precisely once and return to a starting vertex? For a fixed <em>k/, is it possible to “color” the vertices using /k</em> colors so that no two vertices that share an edge receive the same color? More formally, we study the following topics: trees, distance, degree sequences, matchings, connectivity, coloring, and planarity. Proof writing is emphasized. (MATH 0122 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2011, Spring 2014</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0247">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0345 - Combinatorics
</h5>
<div class='coursedesc'>
<p><strong>Combinatorics</strong> <br />
Combinatorics is the “art of counting.” Given a finite set of objects and a set of rules placed upon these objects, we will ask two questions. Does there exist an arrangement of the objects satisfying the rules? If so, how many are there? These are the questions of existence and enumeration. As such, we will study the following combinatorial objects and counting techniques: permutations, combinations, the generalized pigeonhole principle, binomial coefficients, the principle of inclusion-exclusion, recurrence relations, and some basic combinatorial designs. (MATH 0200 or by waiver) 3 hrs. lect./disc. <strong>DED</strong>
</p>
<p>Fall 2012, Spring 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0345">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0500 - Advanced Study
<span title="Offered in the upcoming term[s]">▹</span> </h5>
<div class='coursedesc'>
<p><strong>Advanced Study</strong><br />
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc. </p>
<p>Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Spring 2016</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0500">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 0704 - Senior Seminar
</h5>
<div class='coursedesc'>
<p><strong>Senior Seminar</strong><br />
Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc. </p>
<p>Spring 2015</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH0704">More Information »</a></p>
</div>
<h5 class='coursetitle'>MATH 1007 - Combinatorial Gardner
</h5>
<div class='coursedesc'>
<p><strong>The Combinatorial Gardner</strong><br />
It has been said that the Mathematical Games column written by Martin Gardner for Scientific American turned a generation of children into mathematicians and mathematicians into children. In this course we will read selections from three decades of this column, focusing on those that deal with combinatorics, the “science of counting,” and strive to solve the problems and puzzles given. An example problem that illustrates the science of counting is: what is the maximum number of pieces of pancake (or donut or cheesecake) one can obtain via n linear (or planar) cuts? (MATH 0116 or higher; Not open to students who have taken FYSE 1314). <strong>DED WTR</strong>
</p>
<p>Winter 2013</p>
<p><a href="http://catalog.middlebury.edu/courses/view/catalog/catalog%2FMCUG/course/course%2FMATH1007">More Information »</a></p>
</div>
</div></div></div>Tue, 10 Nov 2009 20:03:00 +0000Benjamin Molberger bmolberg@middlebury.edu21051 at http://www.middlebury.edu