Peter Schumer
Baldwin Professor of Mathematics & Natural Philosophy
Email: schumer@middlebury.edu
Phone: work802.443.5560
Office Hours: on leave Academic Year 2011-12
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Peter Schumer is a Professor of Mathematics and is currently the John C. Baldwin Professor of Mathematics and Natural Philosophy. He has been at Middlebury College since 1983 after receiving his B.S. and M.S. degrees from Rensselaer Polytechnic Institute and a Ph.D. from University of Maryland at College Park.
He is the author of two books, Introduction to Number Theory (PWS) and Mathematical Journeys (Wiley) in addition to many articles in the fields of number theory and the history of mathematics. He is also the recipient of the Trevor Evans Award of the Mathematical Association of America for his article, "The Magician of Budapest".
He has had sabbaticals at University of California San Diego, San Jose State University, Stanford, and at Keio University and Doshisha University in Japan. Hobbies include playing go, juggling, seeing the latest films, travel, and hiking trails around Middlebury.
Courses
Courses offered in the past four years.
▲ indicates offered in the current term
▹ indicates offered in the upcoming term[s]
FYSE 1175 / MATH 1001 - The Game of Go ▹
MATH 0121 - Calculus I
Calculus I
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.
Fall 2010
MATH 0122 - Calculus II
Calculus II
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.
Spring 2009, Spring 2010, Spring 2011
MATH 0200 - Linear Algebra
Linear Algebra
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.
Fall 2008, Fall 2009
MATH 0241 - Elementary Number Theory ▹
Elementary Number Theory
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)
Fall 2010, Fall 2012
MATH 0261 - History of Mathematics
History of Mathematics
This course studies the history of mathematics chronologically beginning with its ancient origins in Babylonian arithmetic and Egyptian geometry. The works of Euclid, Apollonius, and Archimedes and the development of ancient Greek deductive mathematics is covered. The mathematics from China, India, and the Arab world is analyzed and compared. Special emphasis is given to the role of mathematics in the growth and development of science, especially astronomy. European mathematics from the Renaissance through the 19th Century is studied in detail including the development of analytic geometry, calculus, probability, number theory, and modern algebra and analysis. (MATH 0122 or waiver)
Spring 2010
MATH 0302 - Abstract Algebra I
Abstract Algebra
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.
Fall 2008
MATH 0325 - Complex Analysis
Complex Analysis
An introduction to functions of a complex variable. Mappings of the complex plane, analytic functions, Cauchy Integral Theorem and related topics. (MATH 0223 or by waiver) 3 hrs. lect./disc.
Spring 2011
MATH 0500 - Advanced Study ▹
Advanced Study
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.
Fall 2008, Winter 2009, Spring 2009, Fall 2009, Winter 2010, Spring 2010, Fall 2010, Winter 2011, Spring 2011, Fall 2012, Spring 2013