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 offered in the past four years.
▲ indicates offered in the current term
▹ indicates offered in the upcoming term[s]
FYSE 1175 - The Game of Go
The Game of Go
Go is an ancient board game which originated in East Asia and is now played and studied by over 30 million people worldwide. The game is intellectually demanding and rigorous as well as highly creative and intuitive. In this seminar we will study the fundamentals of play, record and critique our games, and learn the history of Go and some of its outstanding practitioners. Additionally, we will gain some appreciation of Asian arts and cultures through our readings and writing projects. There will be plenty of game practice, analysis, some film and anime discussion, and a class tournament. 3 hrs. sem. AAL CW DED
Fall 2012, Fall 2014
MATH 0121 - 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. DED
Spring 2014, Spring 2016
MATH 0122 - 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. DED
Spring 2013, Fall 2013, Spring 2015
MATH 0200 - 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. DED
MATH 0223 - Multivariable Calculus
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. DED
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) DED
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) CMP DED
MATH 0302 - Abstract Algebra I
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. DED
MATH 0325 - 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. DED
MATH 0345 - Combinatorics ▹
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. DED
MATH 0500 - 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 2012, Spring 2013, Fall 2013, Spring 2014, Fall 2014, Spring 2015, Fall 2015, Spring 2016
MATH 0704 - Senior Seminar
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.