Mathematical Sciences

The study of mathematics encourages the development of skills in analytical thinking and problem solving that have wide applicability. Students who graduate with a major in the department have continued their educations in fields as disparate as mathematics, computer science, physics, operations research, law, business, music, religion, dentistry and medicine; others have accepted employment in a wide variety of occupations. The department has a long tradition of successfully preparing students for the actuarial profession.

Mathematics

A major and minor is offered in Mathematics. The basic sequence of courses for Mathematics majors is MATH 151, 152, 223, 251 and 270. Advanced placement and credit can be granted for satisfactory performance on national or departmental examinations.

Actuarial Science

Actuarial science is a well-established business major that involves the application of mathematics, statistics, finance, insurance, and data science to manage risk in insurance, finance, and other industries. Individuals who work in this field are known as actuaries. They are responsible for analyzing data, developing models, and designing solutions to help individuals and organizations manage risk. Our actuarial curriculum is designed to prepare students for the series of professional examinations needed to be practicing actuaries in insurance companies and consulting firms. It also provides students with a solid foundation in quantitative and critical thinking skills, data analysis skills, and strong communication and business skills necessary to pursue a career in related fields, such as risk management, business analytics, quantitative finance, investment, data science, etc.

Data Science

Numerous inquiries today are advanced through finding the story behind the data; frequently, Data Science builds the road from the what to the why. Through an interdisciplinary approach using Statistics, Mathematics, and Computer Science, this program delivers principles, methodology, and guidelines for conducting data analysis by providing tools, values, and insights. Data Science helps prepare students for success in an increasingly data-driven world, enhances analytical and problem-solving skills, and strengthens communication skills.

Course Catalog

Requirements for a major

Actuarial Science

Total courses required Ten
Core courses
  • MATH 151
  • MATH 152
  • ECON 100
  • MATH 331/BUSA 331
  • MATH 332/BUSA 332 (0.5 credit)
  • MATH 441
  • MATH 442 (0.5 credit)
Other required courses Two (one from each list):
  • One mathematics course at the 200 level (MATH 223, MATH 247 or MATH 270)
  • One course in economics, finance or business at the 200 level (ECON 294, ECON 295, FIN 220 or BUSA 240)

One from the following courses (listed by area of specialization)

  • Data Analytics: MATH 261, MATH 348, BUSA 210, BUSA 310, FIN 355, or CSC 370
  • Finance: MATH 336/BUSA 336, FIN/ECON 293
  • Statistics: MATH 341, ECON 385, ECON 450, FIN/ECON 451
Number 300 and 400 level courses Five
Senior requirement and capstone experience The senior requirement consists of MATH 494 or MATH 495.
Additional information

MATH 332/BUSA 332 and MATH 442 are one-half credit courses and will be offered in the same semester as MATH 331/BUSA 331 and MATH 441 respectively.

A student may not major in both Actuarial Science and in Mathematics. A student may not major in Actuarial Science and minor in Mathematics.

Writing in the Major Actuarial Science majors develop their writing expertise by taking the classes Math 223, or Foundations of Advanced Mathematics, and Math 270, Linear Algebra or Math 336, An introduction to Financial Engineering. In lower level courses, significant emphasis will be placed on what it means to express mathematical thoughts and concepts through writing. In Math 336, emphasis will be placed on writing the project process and analyze the financial data by applying the theorems and techniques learned in class. Students are expected to explain the core mathematical tools and fundamental concepts of financial engineering in their papers. Discussion of writing in Actuarial Science takes place throughout the Actuarial Science curriculum, but receives special emphasis in these courses, where students have many opportunities to revise their writing after receiving feedback from the instructor and to integrate mathematical and financial symbols and prose writing, in the form of a cogent argument. The writing in the major requirement in Actuarial Science culminates in the math senior seminar, where students produce an expository paper of approximately twenty pages.

Actuarial Science (declared prior to July 1, 2023)

Total courses required Ten
Core courses MATH 151, MATH 152, ECON 100
Other required courses
  • One mathematics course at the 200 level (MATH 223, MATH 247, MATH 251 or MATH 270)
  • MATH 331 & MATH 332
  • MATH 441 & MATH 442
  • Either ECON 294 or ECON 295
  • One elective from the following courses: MATH 336, MATH 341, MATH 348, ECON 385, ECON 393 or ECON 450
Number 300 and 400 level courses Five
Senior requirement and capstone experience The senior requirement consists of MATH 494 or MATH 495.
Additional information MATH 332 and MATH 442 are one-half credit courses and will be offered in the same semester as MATH 331 and MATH 441 respectively.

A student may not major in both Actuarial Science and in Mathematics. A student may not major in Actuarial Science and minor in Mathematics.

Recent changes in major Add three 300-level courses in the elective course list and one course in the Senior requirement and Capstone Experience.
Writing in the Major Actuarial Science majors develop their writing expertise by taking the classes Math 223, or Foundations of Advanced Mathematics, and Math 270, Linear Algebra or Math 336, An introduction to Financial Engineering. In lower level courses, significant emphasis will be placed on what it means to express mathematical thoughts and concepts through writing. In Math 336, emphasis will be placed on writing the project process and analyze the financial data by applying the theorems and techniques learned in class. Students are expected to explain the core mathematical tools and fundamental concepts of financial engineering in their papers. Discussion of writing in Actuarial Science takes place throughout the Actuarial Science curriculum, but receives special emphasis in these courses, where students have many opportunities to revise their writing after receiving feedback from the instructor and to integrate mathematical and financial symbols and prose writing, in the form of a cogent argument. The writing in the major requirement in Actuarial Science culminates in the math senior seminar, where students produce an expository paper of approximately twenty pages.

Mathematics

Total courses required Ten
Core courses MATH 151, MATH 152, MATH 223, MATH 251, MATH 270, MATH 495
Other required courses Students planning graduate work in mathematics should include MATH 361 and MATH 371. Students concentrating in actuarial mathematics should include MATH 331 and MATH 441. MATH 341 or MATH 348 is also highly recommended.
Number 300 and 400 level courses Four (not including MATH 495)
Senior requirement and capstone experience MATH 495
Writing in the Major

Mathematics majors develop their writing expertise by taking the classes Math 223, Foundations of Advanced Mathematics, and Math 270, Linear Algebra. In these courses, significant emphasis will be placed on what it means to express mathematical thoughts and concepts through writing. Discussion of writing in Mathematics takes place throughout the mathematics curriculum, but receives special emphasis in these courses, where students have many opportunities to revise their writing after receiving feedback from the instructor and to integrate mathematical symbols and prose writing, in the form of a cogent argument. The writing in the major requirement in Mathematics culminates in the senior seminar, where students produce an expository paper of approximately twenty pages.

Requirements for a minor

Applied Statistics

Total courses required 5
Core courses MATH 141, MATH 151, MATH 341. (ECON 350, BIO 275, PSY 214 may be substituted for MATH 141)
Other required courses Two courses from: MATH 247, MATH 261, MATH 340, MATH 348, MATH 441, MATH 423, ECON 450.
Number 300 and 400 level courses 2

Data Science

Total courses required 5
Core courses MATH 141 or PSY 214 or ECON 350 or BIO 375, MATH 261 or CSC 370, MATH 341 or ECON 385 or ECON 450, CSC 121,CSC 125.
Other required courses
Number 300 and 400 level courses

Mathematics

Total courses required Five
Core courses MATH 151, MATH 152, MATH 223, MATH 270
Other required courses
Number 300 and 400 level courses One

Courses in Mathematical Sciences

MATH 123

Computational Discrete Mathematics

An introduction to the concepts of discrete mathematics with an emphasis on problem solving and computation. Topics are selected from Boolean algebra, combinatorics, functions, graph theory, matrix algebra, number theory, probability, relations and set theory. This course may have a laboratory component.

Distribution Area Prerequisites Credits
Science and Mathematics 1 course

MATH 135

Calculus with Review I

Extensive review of topics from algebra, trigonometry, analytic geometry, graphing and theory of equations. A study of functions, limits, continuity and differentiability of algebraic and transcendental functions with applications. Not open to students with credit in MATH 151 or any higher level calculus course.

Distribution Area Prerequisites Credits
Not open to students with credit in MATH 151 or any higher level calculus course 1 course

MATH 136

Calculus with Review II

A continuation of MATH 135. Topics include further study of differentiation, integration of algebraic and transcendental functions with applications, and techniques of integration. Completion of this course is equivalent to completing MATH 151 and is adequate preparation for any course requiring MATH 151. Prerequisite: MATH 135.

Distribution Area Prerequisites Credits
Science and Mathematics MATH 135 1 course

MATH 141

Stats for Professionals

This course introduces students to elementary probability and data analysis via visual presentation of data, descriptive statistics and statistical inference. Emphasis will be placed on applications with examples drawn from a wide range of disciplines in both physical and behavioral sciences and humanities. Topics of statistical inference include: confidence intervals, hypothesis testing, regression, correlation, contingency tales, goodness of fit and ANOVA. The course will also develop familiarity with the most commonly encountered tables for probability distributions: binomial, normal, chi-squared, student-t and F. Students who have completed or are concurrently enrolled in ECON 350 will only receive one-half credit for MATH 141.

Distribution Area Prerequisites Credits
Science and Mathematics 1 course

MATH 143

Mathematical Modeling

This interdisciplinary course will be an engaging and lively look into modeling of phenomena (like voting theory, game theory, traveling salesman problem, population growth/decay etc.) in natural and social sciences. This course will emphasize relationships between the world in which we live and mathematics and is aimed to develop one's mathematical and problem-solving skills in the process. Topics covered will include Modeling Change, Modeling Process and Proportionality, Model Fitting, Probabilistic Modeling, Modeling with Decision Theory, Optimization of Discrete Models, Game Theory and Modeling Using Graph Theory. It will be beneficial for the student to have knowledge in Algebra and Trigonometry for this course.

Distribution Area Prerequisites Credits
Science and Mathematics 1 course

MATH 145

Calculus for Life Sciences

The proposed two-semester interdisciplinary course lies at the interface of mathematics and biology and it addresses the needs of life sciences freshmen/sophomore students. Differential equations, which are built on calculus, represent one of two powerful tools - the other being applied statistics - for modeling and analysis in quantitative life sciences. The proposed courses will combine mathematical training with extensive modeling of biological and natural phenomena by assuming a style that will maintain rigor without being overly formal. Mathematical topics to be covered in MATH 145 (Calculus for Life Sciences) include functions, basic principles of modeling, limits, continuity, exponential and logarithmic functions, trigonometric functions, rates of change, differentiation, optimization, integration and in MATH 146 (Mathematical Modeling for Life Sciences) includes modeling using differential and difference equations, basic computational methods, functions of several variables, partial derivatives, higher-order approximations.

Distribution Area Prerequisites Credits
Science and Mathematics 1 course

MATH 146

Mathematical Modeling for Life Sciences

Distribution Area Prerequisites Credits
Science and Mathematics 1 course

MATH 151

Calculus I

A study of functions, limits, continuity, differentiation and integration of algebraic and transcendental functions with elementary applications.

Distribution Area Prerequisites Credits
Science and Mathematics 1 course

MATH 152

Calculus II

Techniques of integration, parametric equations, infinite series and an introduction to the calculus of several variables. Prerequisite: MATH 136 or MATH 151.

Distribution Area Prerequisites Credits
Science and Mathematics MATH 136 or MATH 151 1 course

MATH 197

First-Year Seminar

The basic approach in this course will be to present mathematics in a more humanistic manner and thereby provide an environment where students can discover, on their own, the quantitative ideas and mathematical techniques used in decision-making in a diversity of disciplines. Students work with problems obtained from industry and elsewhere.

Distribution Area Prerequisites Credits
1 course

MATH 223

Foundations of Advanced Mathematics

An introduction to concepts and methods that are fundamental to the study of advanced mathematics. Emphasis is placed on the comprehension and the creation of mathematical prose, proofs, and theorems. Topics are selected from Boolean algebra, combinatorics, functions, graph theory, matrix algebra, number theory, probability, relations, and set theory. Prerequisite: MATH 123 or MATH 136 or MATH 151.

Distribution Area Prerequisites Credits
Science and Mathematics MATH 123 or MATH 136 or MATH 151 1 course

MATH 247

Mathematical Statistics

This course introduces students to the theory behind standard statistical procedures. The course presumes a working knowledge of single-variable calculus on the part of the student. Students are expected to derive and apply theoretical results as well as carry out standard statistical procedures. Topics covered will include moment-generating functions, Gamma distributions, Chi-squared distributions, t-distributions, and F-distributions, sampling distributions and the Central Limit Theorem, point estimation, confidence intervals, and hypothesis testing. Prerequisite: MATH 136 or MATH 151.

Distribution Area Prerequisites Credits
Science and Mathematics MATH 136 or MATH 151 1 course

MATH 251

Calculus III

An introduction to the calculus of several variables. Topics include vectors and solid analytic geometry, multidimensional differentiation and integration, and a selection of applications. Prerequisite: MATH 152.

Distribution Area Prerequisites Credits
Science and Mathematics MATH 152 1 course

MATH 261

Introduction to Data Science

This course provides an introduction to the field of data science from data to knowledge and gives students' hands-on experience with tools and methods. This course focuses on using computational, statistical, and mathematical tools for data acquisition, exploration, manipulation, visualization, analysis, modeling, and classification, as well as the communication of results. Prerequisite: MATH 141 (or equivalent) or permission of instructor.

Distribution Area Prerequisites Credits
MATH 141 (or equivalent) or permission of instructor 1 course

MATH 270

Linear Algebra

Vector spaces, linear transformations, matrices, determinants, eigenvalues and eigenvectors and applications. Prerequisite: MATH 152 or permission of instructor.

Distribution Area Prerequisites Credits
MATH 152 or permission of instructor 1 course

MATH 321

Topics in Geometry

Selections from advanced plane, differential, non-Euclidean or projective geometry. Prerequisite: either MATH 223 or MATH 270.

Distribution Area Prerequisites Credits
Either MATH 223 or MATH 270 1 course

MATH 323

Algorithmic Graph Theory

Algorithmic Graph Theory is that branch of Mathematics that deals with mathematical structures that are used to model pairwise relations between objects from a certain collection, together with algorithms used to manipulate these models. Algorithmic Graph Theory is used to model many types of relations and process dynamics in physical, biological and social systems. This course helps students develop the mathematical underpinnings of the theory of graphs and algorithms, a branch of discrete mathematics. This course provides an excellent background to an exciting area of mathematics that has applications in fields like computer science, economics, and engineering. Prerequisites: CSC 233, foundations of computation or MATH 270, linear algebra or MATH 223, foundations of advanced mathematics. It will be beneficial for the student to be fluent in a programming language for this course.

Distribution Area Prerequisites Credits
Science and Mathematics CSC 233, Foundations of Computation or MATH 270, Linear Algebra or MATH 223, Foundations of Advanced Mathematics. 1 course

MATH 331

Financial Mathematics

Dive into the world of financial mathematics and unlock the power of money over time. This course equips students with advanced mathematical skills to navigate complex financial landscapes. Master the art of calculating the time value of money, analyzing investment opportunities, and understanding the intricacies of loans and bonds. Explore yield curves, portfolio management, and asset-liability matching techniques used by financial professionals. Gain hands-on experience with real-world applications in investment analysis, capital budgeting, and risk management. Upon completing this course, students will be able to navigate financial decisions confidently and strategically in an ever-evolving economic landscape. Prerequisite: ECON 100 and MATH 136 or MATH 151 or ECON 375

Distribution Area Prerequisites Credits
ECON 100 and MATH 136 or MATH 151 or ECON 375 1 course

MATH 332

Seminar in Financial Mathematics

This is a problem-solving seminar. The problems discussed in the seminar provide students with a better understanding of the actuarial field by exposing students to the professional application of actuarial science and by providing resources for students taking actuarial exams. Techniques and strategies for solving difficult problems are also introduced in the seminar. The seminar also includes an introduction of financial instruments, the determinants of interest rates, an alternative way to approximate the effect of change in interest rates, and interest rate swaps. This course is of great assistance for students who are preparing for the actuarial exam Financial Math. Prerequisite: MATH 331 which may be taken concurrently.

Distribution Area Prerequisites Credits
MATH 331 which may be taken concurrently. 1/2 course

MATH 336

Quantitative Risk Analysis

This course in Quantitative Risk Analysis provides students with a comprehensive interdisciplinary foundation in quantitative techniques for financial risk assessment and management. The curriculum encompasses the principles of fixed-income securities, Modern Portfolio Theory (MPT) and advanced topics like the Black-Scholes formula and the Binomial Tree method for derivatives pricing. The course emphasizes practical skills in identifying, calculating, and mitigating risks associated with fixed-income securities, equities, options, and futures. Students will work on projects that simulate real-world scenarios, gaining experience in managing the interest rate risk of fixed-income securities by controlling durations, applying MPT to create efficient portfolios, using stock index futures to manage market exposure, and leveraging stock options to hedge individual stock risks. Prerequisite: MATH 136 or MATH 151 or ECON 375, ECON 100, and either MATH 141 or ECON 350.

Distribution Area Prerequisites Credits
Math 136 or MATH 151 or ECON 375, Econ 100, and either MATH 141 or ECON 350 1 course

MATH 340

Topics in Statistics

Topics in statistics.

Distribution Area Prerequisites Credits
1/4-1/2-1 course

MATH 341

Statistical Model Analysis

This course is designed to provide students with a solid overview of basic and advanced topics in regression analysis. This course mainly covers the simple and multiple linear regression models--method of least squares, model and assumptions; testing hypotheses; estimation of parameters and associated standard errors; correlations between parameter estimates; standard error of predicted response values; inverse prediction; regression through the origin; matrix approach; extra sum of squares principle as used in model building; partial F-tests and sequential F-tests. More advanced topics in regression analysis, such as selecting the 'best' regression equation, classical approaches: all possible regressions; backward elimination; forward selection; stepwise regression; indicator (dummy) variables in regression also introduces in this course. Additionally, nonlinear (binary) logistic regression model with qualitative independent variables discusses in this course. A statistical computing package, such as R, is used throughout the course. Prerequisite: MATH 141 or ECON 350 or PSY 214 or BIO 275

Distribution Area Prerequisites Credits
Science and Mathematics MATH 141 or ECON 350 or PSY 214 or BIO 275 1 course

MATH 348

Introduction to Statistical Computing

This course is designed to provide students with an introduction to statistical computing using RStudio. This course will have two components. In the first part of the course, students will learn data manipulations, data structures, matrix manipulation, database operation, and functions. In the second part of the course, students will learn statistical computing topics including simulation studies and Monte Carlo methods, numerical optimization, Bootstrap resampling methods, and visualization. Students will be introduced to some packages and technologies that are useful for statistical computing. Through producing numerical summaries and creating customized graphs, students will be able to discuss the results obtained from their analyses and to generate dynamic and reproducible documents. Prerequisites: Math 141 (or ECON 350/BIO 375/PSY 214) and Math 151 (or MATH 135-136).

Distribution Area Prerequisites Credits
Science and Mathematics Math 141 (or ECON 350/BIO 375/PSY 214) and Math 151 (or MATH 135-136) 1 course

MATH 361

Analysis

A study of the theory of limits, continuity, differentiation, integration, sequences and series. Prerequisite: MATH 152 and either MATH 223 or MATH 270.

Distribution Area Prerequisites Credits
MATH 152 and either MATH 223 or MATH 270 1 course

MATH 363

Differential Equations

Equations of the first degree, linear differential equations, systems of equations with matrix methods and applications. Selected topics from power series solutions, numerical methods, boundary-value problems and non-linear equations. Prerequisites: MATH 152 and MATH 270.

Distribution Area Prerequisites Credits
MATH 152 and MATH 270 1 course

MATH 367

Introduction to Numerical Analysis

Analysis of algorithms frequently used in mathematics, engineering and the physical sciences. Topics include sources of errors in digital computers, fixed point iteration, interpolation and polynomial approximation, numerical differentiation and integration, direct and iterative methods for solving linear systems, and iterative methods for nonlinear systems. Numerical experiments will be conducted using FORTRAN, C, or another appropriate high-level language. Prerequisites: MATH 270 and CSC 121 or permission of instructor.

Distribution Area Prerequisites Credits
MATH 270 and CSC 121 or permission of instructor 1 course

MATH 371

Algebraic Structures

The structure of groups, group homomorphisms and selected topics from other algebraic structures, such as rings, fields and modules. Prerequisite: MATH 270.

Distribution Area Prerequisites Credits
MATH 270 1 course

MATH 382

Number Theory

Divisibility and factorization of integers, linear and quadratic congruences. Selected topics from diophantine equations, the distribution of primes, number-theoretic functions, the representation of integers and continued fractions. Prerequisite: MATH 270 or permission of instructor.

Distribution Area Prerequisites Credits
MATH 270 or permission of instructor 1 course

MATH 390

Advanced Topics in Mathematics

A. Actuarial Mathematics; B. Algebra; C. Analysis; D. Foundations of Mathematics; E. Geometry; F. Applied Mathematics; G. Special Topics.

Distribution Area Prerequisites Credits
1/2 - 1

MATH 422

Operations Research

Topics selected from linear and dynamic programming, network analysis, game theory and queueing theory are applied to problems in production, transportation, resource allocation, scheduling and competition. Prerequisite: MATH 270.

Distribution Area Prerequisites Credits
MATH 270 1 course

MATH 423

Advanced Topics in Operations Research

Advanced topics in linear programming, integer programming, nonlinear programming, game theory, Markov chains, and dynamic programming. Prerequisite: MATH 422

Distribution Area Prerequisites Credits
Math 422 1 course

MATH 441

Probability

Probability, sample spaces and events, discrete and continuous random variables, density and their distributions, including the binomial, Poisson and normal. Prerequisite: MATH 152 and MATH 223.

Distribution Area Prerequisites Credits
MATH 152 and MATH 223 1 course

MATH 442

Probability Problems Seminar

The seminar will include the topics of multivariate distributions, order statistics, the law of large numbers, basic insurance policies, frequency of loss, frequency distribution, severity, severity distribution, characteristics of an insurable risk, measurement of risk, economics risk, expected value of loss, loss distribution, premium payment, claim payment distribution, limits on policy benefit (deductible, maximum, benefit limits) and role of actuaries. After studying, students will be able to demonstrate a solid foundation in probability by their ability to solve a variety of basic and advanced actuarial practical problems. Prerequisite: MATH 441 which may be taken concurrently.

Distribution Area Prerequisites Credits
MATH 441 which may be taken concurrently 1/2 course credit

MATH 490

Mathematics Topics

A. Actuarial Mathematics; B. Algebra; C. Analysis; D. Foundations of Mathematics; E. Geometry; F. Probability and Statistics; G. Applied Mathematics; H. Special Topics. Prerequisite: permission of instructor. May be repeated for credit with different topics.

Distribution Area Prerequisites Credits
Permission of instructor 1/2-1 course

MATH 494

Actuarial and Risk Management Case Studies

This senior capstone course emphasizes group work and discussions, allowing students to apply actuarial models, risk analysis techniques, and risk management strategies to various insurance domains, including Auto, Health, Life, and Property & Casualty, etc. Students will collaborate in groups on projects utilizing public data from the Society of Actuaries, Casualty Actuarial Society, and other industry resources to model, price insurance products, mitigate risks through risk identification, assessment, and control measures, and develop risk management plans. Through these projects, students will leverage statistical, analytical, and data analytics methods to conduct research on real-world datasets, gaining practical experience in addressing complex actuarial, risk management, and risk financing challenges while enhancing problem-solving, teamwork, communication, and risk management skills essential for future careers in the insurance and financial industry. Prerequisite: MATH/BUS 331 or MATH/BUS 336, MATH 441, and one upper-level statistics course from the list (MATH 341, MATH 348, BUS 305, ECON 385, ECON 450, FIN 451).

Distribution Area Prerequisites Credits
MATH/BUS 331 or MATH/BUS 336, MATH 441, and one upper-level statistics course from the list (MATH 341, MATH 348, BUS 305, ECON 385, ECON 450, FIN 451) 1 course

MATH 495

Seminar: Mathematics

Advanced topics considered individually or in small groups. Open only to senior Mathematics majors or by permission of the Department of Mathematics.

Distribution Area Prerequisites Credits
1 course