Peter Schumer
Office
Warner 209
Tel
(802) 443-5560
Email
schumer@middlebury.edu
Office Hours
On leave academic year 2022/2023
Additional Programs
Mathematics

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
Go is an ancient board game which originated in East Asia and is now played and studied by over 40 million people worldwide. The game is both intellectually demanding and rigorous as well as artistic and highly creative. 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 a deeper appreciation of Asian arts and cultures through our readings, learning journals, writing projects, and presentations. There will be plenty of game practice, analysis, some film and anime discussion, and a class tournament. 3 hrs. Sem

Terms Taught

Fall 2018

Requirements

AAL, CW, DED, NOA

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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. 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. 4 hrs. lect.

Terms Taught

Fall 2018, Fall 2019, Spring 2020, Fall 2021

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 by waiver) 3 hrs. lect./disc.

Terms Taught

Spring 2019, 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

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.

Terms Taught

Spring 2019

Requirements

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

Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022, Spring 2023

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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 2019, Fall 2021

Requirements

DED

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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