Peter Schumer
Office
Warner 209
Tel
(802) 443-5560
Email
schumer@middlebury.edu
Office Hours
By appointment

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 has been the recipient of the Trevor Evans Award of the Mathematical Association of America for his article, “The Magician of Budapest” as well as having received the North American Teacher of the Year award from the American Go Federation.

Pete has had sabbaticals at University of California San Diego, San Jose State University, Stanford, and at Keio University, Doshisha University, and International Christian University in Japan.  Hobbies include playing go, juggling, seeing the latest films, travel, and hiking trails around Middlebury.

Courses Taught

Course Description

The Game of Go within Traditional Japanese Culture
The ancient East Asian game of go will be introduced, studied, and developed within the context of Japanese history and cultural traditions – especially that of the Edo Period. Game play, careful analysis, and problem solving will be a key component of the course. Additionally, the art and aesthetics of Japanese gardens and woodblock prints will be studied by the class as preparation for individual research and presentation of an East Asian art form or tradition. (not open to students who have taken FYSE 1175)

Terms Taught

Spring 2022

Requirements

DED, NOA

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Course Description

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. (by waiver) 4 hrs. lect./disc.

Terms Taught

Fall 2020

Requirements

DED

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Course Description

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 equivalent) 4 hrs. lect/disc.

Terms Taught

Spring 2020, Fall 2021, Fall 2023

Requirements

DED

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Course Description

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 equivalent) 3 hrs. lect./disc.

Terms Taught

Spring 2021, Spring 2022

Requirements

DED

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Course Description

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)

Terms Taught

Spring 2020

Requirements

DED

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Course Description

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)

Terms Taught

Fall 2020

Requirements

CMP, DED

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Course Description

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.

Terms Taught

Spring 2021

Requirements

DED

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Course Description

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.

Terms Taught

Spring 2020, Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022, Fall 2023, Spring 2024, Fall 2024, Spring 2025

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Course Description

Advanced Number Theory
A senior tutorial on some topics in advanced elementary number theory and an introduction to analytic number theory. In this course we will review key areas of elementary number theory and abstract algebra followed by the study of integer partitions, continued fractions, rational approximations of irrationals, primes and primality testing, the average order of magnitude of several number theoretic functions, the Basel problem, Bernoulli numbers, and the Riemann zeta function. (MATH 0241 or MATH 0302) 3 hrs. sem.

Terms Taught

Fall 2021, Fall 2023

Requirements

DED

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Course Description

Math Circus
Each class will entail small group work solving various logic and puzzle problems, mathematical conundrums, and devising winning strategies for various games and challenges. Students will present their solutions to the class and work on their own puzzles and games pamphlet to be completed by the end of the term. Elementary mathematical, logical, game theoretic, and probability concepts will be introduced as needed with the goal of increasing everyone's problem solving and analytical thinking skills. The class will meet four days a week (2 hours per class).

Terms Taught

Winter 2024

Requirements

DED, WTR

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Academic Degrees

B.S. and M.S. degrees from Rensselaer Polytechnic Institute and a Ph.D. from University of Maryland at College Park

Publications