The study of vector spaces over the real and complex numbers, introducing the concepts of subspace, linear independence, basis, and dimension; systems of linear equations and their solution by Gaussian elimination; matrix operations; linear transformations and their representations by matrices; eigenvalues and eigenvectors; and inner product spaces. MATH 271 will feature both proofs and applications, with special attention paid to the theoretical development of the subject. Four class meetings per week.

The study of vector spaces over the real and complex numbers, introducing the concepts of subspace, linear independence, basis, and dimension; systems of linear equations and their solution by Gaussian elimination; matrix operations; linear transformations and their representations by matrices; eigenvalues and eigenvectors; and inner product spaces. MATH 271 will feature both proofs and applications, with special attention paid to the theoretical development of the subject. Four class meetings per week.

The study of differential equations is an important part of mathematics that involves many topics, both theoretical and practical. The course will cover first- and second-order ordinary differential equations, basic theorems concerning existence and uniqueness of solutions and continuous dependence on parameters, long-term behavior of solutions and approximate solutions. Four class hours per week.

Requisite: MATH 211 or consent of the instructor. Limited to 25 students. Spring semester. Professor Folsom.

Many security problems arise when two computers must communicate on a channel with eavesdroppers or malicious attackers. Public-key cryptography applies ideas from number theory and abstract algebra to address these problems. This course concerns the mathematical theory and algorithms needed to construct the most commonly-used public-key ciphers and digital signature schemes, as well as the attacks that must be anticipated when designing such systems.

An introduction to the theory of rational integers; divisibility, the unique factorization theorem; congruences, quadratic residues. Selections from the following topics: cryptology; Diophantine equations; asymptotic prime number estimates; continued fractions; algebraic integers. Four class hours per week. Offered in alternate years.

Requisite: MATH 121 or consent of the instructor. Limited to 25 students. Spring semester. Professor Call. 

How to handle overenrollment: Preference is given to math majors.

This course is a mathematical treatment of fractal geometry, a field of mathematics partly developed by Benoit Mandelbrot (1924–2010) that continues to be actively researched in the present day. Fractal geometry is a mathematical examination of the concepts of self-similarity, fractals, and chaos, and their applications to the modeling of natural phenomena. In particular, we will develop the iterated function system (IFS) method for describing fractals, examine Julia sets, Mandelbrot sets, and study the concept of fractal dimension, among other things.

This course serves as an introduction to mathematical reasoning and pays particular attention to helping students learn how to write proofs. The topics covered may include logic, elementary set theory, functions, relations and equivalence relations, mathematical induction, sequences, and quantifiers. Additional topics may vary from semester to semester. Four class hours per week.

Limited to 25 students. Spring and fall semesters. The Department. 

This course serves as an introduction to mathematical reasoning and pays particular attention to helping students learn how to write proofs. The topics covered may include logic, elementary set theory, functions, relations and equivalence relations, mathematical induction, sequences, and quantifiers. Additional topics may vary from semester to semester. Four class hours per week.

Limited to 25 students. Spring and fall semesters. The Department. 

Elementary vector calculus; introduction to partial derivatives; multiple integrals in two and three dimensions; line integrals in the plane; Green’s theorem; the Taylor development and extrema of functions of several variables; implicit function theorems; Jacobians. Four class hours per week.

Requisite: A grade of C or better in MATH 121 or placement into MATH 211 or consent of the Department. Limited to 30 students per section. Fall and spring semesters. The Department.

Elementary vector calculus; introduction to partial derivatives; multiple integrals in two and three dimensions; line integrals in the plane; Green’s theorem; the Taylor development and extrema of functions of several variables; implicit function theorems; Jacobians. Four class hours per week.

Requisite: A grade of C or better in MATH 121 or placement into MATH 211 or consent of the Department. Limited to 30 students per section. Fall and spring semesters. The Department.