Bachelor of Science in Pure and Applied Mathematics

Mathematics, as Galileo said, is the language in which the universe is written. It is a subject of great beauty, utility, and scope that is not only fundamental to all other disciplines in STEM but fascinating in its own right. Exploring mathematics in its many forms within a community of like-minded peers fosters creativity, critical thinking, and collaboration, thereby equipping students with tools to succeed in a wide range of settings.

The Bachelor of Science in Pure and Applied Mathematics offers a broad background in mathematics appropriate for students planning to pursue a career in industry while providing the depth and rigor required for graduate studies in mathematics or related fields. Students majoring in Pure and Applied Mathematics may concentrate their studies in one of several areas, including pure mathematics, cryptography, computational mathematics, and data science. With a first-year math seminar, a senior research project, and a large number of elective courses in between, the program gives students ample opportunities to pursue their interests.

The undergraduate program in Pure and Applied Mathematics has the following objectives and outcomes.

Program Objectives

  • Graduates choosing academic careers in mathematics are successful as Ph.D. candidates in internationally recognized programs in mathematics or related fields.
  • Graduates find rewarding careers where they are able to apply their knowledge and skills in the mathematical sciences to solving problems in mathematics, science, engineering, business, and education.
  • Graduates demonstrate strong teamwork and leadership skills in solving complex mathematical and multidisciplinary problems.
  • Graduates employ a variety of technologies and computational platforms to assist in solving and understanding mathematical problems.
  • Graduates participate in the activities of professional organizations relevant to their chosen field.

Program Outcomes

  • Mathematics Foundations. Graduates will understand important definitions and theorems across core branches of mathematics, including calculus, linear algebra, abstract algebra, probability and statistics, and analysis.
  • Comprehension and Analysis. Graduates will be able to explain and restate theorems, concepts, and methods in different contexts, and recognize which results are relevant to various situations.
  • Applications. Graduates will be able to apply mathematical reasoning, theories, and techniques to analyze and solve problems in mathematics, science, engineering, and business.
  • Synthesis. Graduates will be able to construct complex mathematical arguments from previously acquired knowledge, and bring together knowledge from different areas of mathematics to analyze and solve mathematical problems.
  • Computation. Graduates will have basic knowledge in the theory of computation and data structures, be familiar with commonly used algorithms in computational mathematics, and proficient in at least one programming language or computational platform.
  • Modeling. Graduates will understand common models used in the applied sciences and be experienced in constructing mathematical and numerical models.
  • Communication. Graduates will be able to communicate effectively and persuasively when presenting technical results.
  • Professionalism. Graduates will recognize and achieve high levels of professionalism in their work.
  • Teamwork. Graduates will be able to function effectively on multidisciplinary teams.
  • Lifelong Learning. Graduates will recognize the need for and have the ability to engage in lifelong learning and development through further education and participation in professional organizations.

Mathematics Curriculum

The undergraduate curriculum in Pure and Applied Mathematics consists of:

  • 19 core courses in mathematics spanning a wide range of mathematical disciplines and culminating in a research project conducted in the senior year
  • 6 elective math courses (called technical electives) that may be chosen by the student and that may include graduate courses
  • 6 science courses and 1 science lab, including courses on physics, chemistry, and computer science, and including 2 science electives that may be chosen by the student
  • 6 humanities courses, 4 of which are electives that may be chosen by the student
  • 1 course on either macroeconomics or microeconomics
  • 5 additional elective courses that may be chosen by the student to pursue other academic goals, such as a minor, double major, master's degree, or simply acquiring knowledge in particular fields of interest

See below for a sample study plan, and note that courses do not need to be taken in exactly the order shown here. Students with AP credit (for the calculus courses MA 121 and MA 122, for instance) may take more advanced courses (such as MA 125 and MA 126) in their first semester. Students should meet with an academic advisor to determine how best to meet the program requirements and how to choose electives so as to achieve their academic goals. See the notes following the sample study plan for more details on the program requirements. Math majors should submit an approved study plan in Term II.

Term I

MA 121Differential Calculus

2

MA 122Integral Calculus

2

CH 115General Chemistry I

3

CS 115Introduction to Computer Science

4

PEP 111Mechanics

3

CAL 103Writing and Communications Colloquium

3

Science Lab

1

Term II

MA 125Vectors and Matrices

2

MA 126Multivariable Calculus I

2

MA 188Seminar in Mathematical Sciences

1

PEP 112Electricity and Magnetism

3

CAL 105CAL Colloquium: Knowledge, Nature, Culture

3

Science Elective

3

Term III

MA 221Differential Equations

4

MA 225Infinite Series

2

MA 226Multivariable Calculus II

2

BT
Economics

3

Humanities Elective

3

General Elective

3

Term IV

MA 222Probability and Statistics

3

MA 231Nonlinear Optimization

2

MA 232Linear Algebra

3

MA 240Proofs and Refutations

3

Humanities Elective

3

General Elective

3

Term V

MA 234Complex Variables with Applications

3

MA 331Intermediate Statistics

3

MA 441Introduction to Mathematical Analysis

3

Technical Elective

3

Humanities Elective

3

Term VI

MA 336Modern Algebra

3

MA 346Numerical Methods

3

Technical Elective

3

Free Technical Elective

3

Science Elective

3

Term VII

MA 410Differential Geometry

3

MA 498Senior Research Project I

3

Technical Elective

3

Free Technical Elective

3

Humanities Elective

3

Term VIII

Technical Elective

3

Technical Elective

3

Technical Elective

3

General Elective

3

Notes

Preapproved technical electives include MA 134, MA 335, MA 360, MA 361, MA 442, MA 463, MA 464, MA 499, MA 503, MA 525, MA 526, MA 544, MA 550, MA 552, MA 564, MA 565, MA 567, and MA 575. Students who wish to count a course not on this list as a technical elective should speak with an academic advisor.

To satisfy the senior research requirement, students may take MA 498, which is offered in the fall term, or MA 499, which is offered in the spring term. Students may take both and count MA 499 as a technical elective.

To satisfy the science requirements, students must take CH 115, CS 115, PEP 111, and PEP 112. They must also take one science lab, which may be CH 117, PEP 221, or BIO 282, and two additional science electives, one of which must be at the 200-level or higher. Science electives may include computer science courses.

To satisfy the humanities requirements, students must take CAL 103, CAL 105, and four additional humanities electives, one of which must be at the 300-level or higher. For more information on humanities requirements and electives, see the Humanities Requirements page maintained by the College of Arts and Letters.

To satisfy the economics requirement, students may take BT 243 or BT 244. Students who take both courses may use one in place of a 200-level humanities elective.

Free technical electives may be any 3-credit courses at the 300-level or higher. General electives may be any 3-credit courses. They may include courses used to fulfill minor, double major, or master's degree requirements, as well as language courses or courses taken while studying abroad.