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Bachelor of Science in 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. Undergraduate students majoring in Mathematics benefit from a unique curriculum that leverages the research strengths of the department and offers great flexibility.

Program Description

The Bachelor of Science in Mathematics program 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 Mathematics may concentrate their studies in one of several areas, including pure mathematics, data science, and computational algebra. Moreover, the program gives students ample opportunities to pursue their interests, in particular through its research spine, a sequence of courses integrated into each year of the curriculum that gives all students the opportunity to conduct original mathematical research.

Areas of Concentration

  • Pure Mathematics
  • Data Science
  • Computational Algebra

Mathematics Research Spine

  • First Year: MA 188 (Seminar in Mathematical Sciences)
    Students gain exposure to the research interests of math faculty and explore a mathematical topic or problem with peers.
  • Sophomore Year: MA 240 (Proofs and Refutations)
    Students receive extensive training in writing mathematical proofs at a high level of quality and rigor, learn the mathematical typesetting software LaTeX, and write a paper on a mathematical theorem.
  • Junior Year: MA 398 (Introduction to Mathematical Research)
    Students learn about key elements of conducting mathematical research, including formulating a research problem and navigating published literature, and collaborate on a mini research project.
  • Senior Year: MA 498 (Senior Research Project I)
    Students work individually or as part of a team to conduct an original research project in an area of mathematics of interest to them under the supervision of a math faculty member. The results of the project are disseminated via a research report and a presentation, e.g. at the annual Innovation Expo. Students wishing to pursue a full year of senior research may continue with the course MA 499 (Senior Research Project II).

Program Objectives and Outcomes

The Bachelor of Science in Mathematics program 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 Mathematics consists of:

  • 21 core courses in mathematics spanning a wide range of mathematical disciplines and culminating in a research project conducted in the senior year
  • 5 elective math courses (called technical electives) that may be chosen by the student and that may include graduate courses
  • 5 science courses and 1 science lab, including courses on computer science and physics, and including 2 science electives that may be chosen by the student
  • 5 humanities courses, 3 of which are electives that may be chosen by the student
  • 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
  • 5 courses that comprise the SUCCESS core curriculum, including 4 seminars and 1 course on entrepreneurship
  • 1 course on either macroeconomics or microeconomics

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.

Term I

MA 121Differential Calculus

2
MA 122Integral Calculus

2
MA 188Seminar in Mathematical Sciences

1
CS 115Introduction to Computer Science

4
PEP 111Mechanics

3
HASS 103Writing and Communications Colloquium

3
PRV 101First Year Experience

1

Term II

MA 125Vectors and Matrices

2
MA 126Multivariable Calculus I

2
MA 134Discrete Mathematics

3
PEP 112Electricity and Magnetism

3
Science Elective

3
Science Lab

1
HASS 105Knowledge, Nature, Culture

3

Term III

MA 221Differential Equations

4
MA 225Infinite Series

2
MA 226Multivariable Calculus II

2
Science Elective

3
Humanities Elective

3
MGT 103Introduction to Entrepreneurial Thinking

2
PRV 20XFrontiers of Technology

1

Term IV

MA 222Probability and Statistics

3
MA 232Linear Algebra

3
MA 240Proofs and Refutations

3

BT 243Macroeconomics

3
Or
BT 244Microeconomics

3

Humanities Elective

3
PRV 20XFrontiers of Technology

1

Term V

MA 231Nonlinear Optimization

2
MA 331Intermediate Statistics

3
MA 398Introduction to Mathematical Research

2
MA 441Introduction to Mathematical Analysis

3
T.E.
Technical Elective

3
T.E.
Free Technical Elective

3
PRV 20XFrontiers of Technology

1

Term VI

MA 234Complex Variables with Applications

3
MA 336Modern Algebra

3
MA 346Numerical Methods

3
T.E.
Technical Elective

3
G.E.
General Elective

3

Term VII

MA 410Differential Geometry

3
MA 498Senior Research Project I

3
T.E.
Technical Elective

3
Humanities Elective

3
G.E.
General Elective

3

Term VIII

T.E.
Technical Elective

3
T.E.
Technical Elective

3
T.E.
Free Technical Elective

3
G.E.
General Elective

3

Notes:

(1) Science Electives: Students must take CS 115, PEP 111, and PEP 112. They must also take one science lab, which may be CH 117, BIO 182, or PEP 221, and two additional science electives, one of which must be at the 200-level or higher. Science electives may include computer science courses or the courses PEP 151 and PEP 152.

(2) Technical Electives may be any 3-credit math courses at the 300-level or higher that are not core program requirements. Pre-approved technical electives include 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, MA 575, MA 576, and MA 577. Students who wish to count a course not on this list as a technical elective should speak with an academic advisor.

Students must take either MA 498 or MA 499 to satisfy the senior research requirement. Students may take both and count MA 499 as a technical elective.

(3) General Electives may be any 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.

(4) SUCCESS Core Curriculum: Students must complete requirements including PRV 101, and three (3) courses from PRV 201, PRV 202, PRV 203, PRV 204, PRV 205.

(5) Humanities: Please see the Humanities Requirements for specific requirements.

Either BT 243 or BT 244 may be taken to satisfy the economics requirement. Students who take both courses may use one in place of a 200-level humanities elective.

Pure Mathematics Concentration Curriculum

Take any three of the following courses:

MA 335Elementary Number Theory

3
MA 442Real Variables

3
MA 550Introduction to Lie Theory

3
MA 552Axiomatic Linear Algebra

3
In consultation with an advisor and upon receiving permission to enroll, students may also count 600-level math courses towards this concentration.

Data Science Concentration Curriculum

Take any two of the following courses:

MA 544Numerical Linear Algebra for Big Data

3
MA 576Optimization for Data Science

3
MA 577Statistical Network Analysis

3
MA 641Time Series Analysis I

3
MA 654Topological Data Analysis

3

And take one of the following machine learning courses:

CS 559Machine Learning: Fundamentals and Applications

3
CPE 595Applied Machine Learning

3

Computational Algebra Concentration Curriculum

Take any three of the following courses:

MA 503Discrete Mathematics for Cryptography

3
MA 552Axiomatic Linear Algebra

3
MA 564Mathematics of Post-Quantum Cryptography

3
MA 565Quantum Algorithms

3
MA 567Computational Algebraic Geometry

3