# Peter Schumer

## Baldwin Professor of Mathematics & Natural Philosophy

schumer@middlebury.edu

work(802) 443-5560

Spring 2020: Monday, Tuesday, Thursday 1:30-3:00 PM, and by appointment

Warner Hall 306

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 - 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 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 **AAL CW DED NOA**

Fall 2018

##### 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. **DED**

Spring 2016, Fall 2020

##### 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. **DED**

Spring 2018, Fall 2018, Fall 2019, Spring 2020

##### 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. **DED**

Fall 2017, Spring 2019

##### 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**

Spring 2020

##### 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**

Spring 2018, Fall 2020

##### 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. **DED**

Fall 2017, Spring 2019

##### MATH 0345 - Combinatorics

**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**

Spring 2016

##### 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.

Spring 2016, Spring 2017, Fall 2017, Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021

##### MATH 0741 - Advanced Number Theory

**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. **DED**

Fall 2019