Mathematics

Course Description

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

Science and Mathematics

Credits

1 course

Fall Semester information

123A: Computational Discrete Math

Professor: Sirous Homayouni,
Naima Shifa

123B: Computational Discrete Math

Professor: Sirous Homayouni,
Naima Shifa

Spring Semester information

123A: Computational Discrete Math

Professor: Suman Balasubramanian

123B: Computational Discrete Math

Professor: Suman Balasubramanian

Course Description

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.

Prerequisites

Not open to students with credit in MATH 151 or any higher level calculus course

Credits

1 course

Fall Semester information

135A: Calculus with Review I

Professor: McKenzie Lamb

135B: Calculus with Review I

Professor: McKenzie Lamb

Course Description

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

Science and Mathematics

Prerequisites

MATH 135

Credits

1 course

Spring Semester information

136A: Calculus with Review II

Professor: McKenzie Lamb,
Naima Shifa

Course Description

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

Science and Mathematics

Credits

1 course

Fall Semester information

141A: Stats for Professionals

Professor: Laien He

141B: Stats for Professionals

Professor: Laien He

141C: Stats for Professionals

Professor: Suman Balasubramanian

Spring Semester information

141A: Stats for Professionals

Professor: Laien He,
Naima Shifa

141B: Stats for Professionals

Professor: Laien He,
Naima Shifa

Course Description

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

Science and Mathematics

Credits

1 course

Course Description

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

Science and Mathematics

Credits

1 course

Course Description

Distribution Area

Science and Mathematics

Credits

1 course

Course Description

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

Distribution Area

Science and Mathematics

Credits

1 course

Fall Semester information

151A: Calculus I

Professor: Scott Hiatt

151B: Calculus I

Professor: Scott Hiatt

151C: Calculus I

Professor: Suman Balasubramanian

Spring Semester information

151A: Calculus I

Professor: Sutthirut Charoenphon

151B: Calculus I

Professor: Sutthirut Charoenphon

151C: Calculus I

Professor: Sirous Homayouni,
Naima Shifa

Course Description

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

Distribution Area

Science and Mathematics

Prerequisites

MATH 136 or MATH 151

Credits

1 course

Fall Semester information

152A: Calculus II

Professor: Sutthirut Charoenphon

152B: Calculus II

Professor: Sutthirut Charoenphon

Spring Semester information

152A: Calculus II

Professor: Scott Hiatt

152B: Calculus II

Professor: Scott Hiatt

Course Description

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.

Credits

1 course

Course Description

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

Science and Mathematics

Prerequisites

MATH 123 or MATH 136 or MATH 151

Credits

1 course

Fall Semester information

223A: Foundations of Advanced Math

Professor: Scott Hiatt

Spring Semester information

223A: Foundations of Advanced Math

Professor: Sirous Homayouni,
Naima Shifa

Course Description

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

Science and Mathematics

Prerequisites

MATH 136 or MATH 151

Credits

1 course

Spring Semester information

247A: Mathematical Statistics

Professor: Naima Shifa

Course Description

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

Science and Mathematics

Prerequisites

MATH 152

Credits

1 course

Fall Semester information

251A: Calculus III

Professor: Sutthirut Charoenphon

Spring Semester information

251A: Calculus III

Professor: Sirous Homayouni,
Naima Shifa

Course Description

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.

Prerequisites

MATH 141 (or equivalent) or permission of instructor

Credits

1 course

Fall Semester information

261A: Intro to Data Science

Professor: Mamunur Rashid

Course Description

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

Prerequisites

MATH 152 or permission of instructor

Credits

1 course

Fall Semester information

270A: Linear Algebra

Professor: Suman Balasubramanian

Spring Semester information

270A: Linear Algebra

Professor: Suman Balasubramanian

Course Description

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

Prerequisites

Either MATH 223 or MATH 270

Credits

1 course

Course Description

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

Science and Mathematics

Prerequisites

CSC 233, Foundations of Computation or MATH 270, Linear Algebra or MATH 223, Foundations of Advanced Mathematics.

Credits

1 course

Course Description

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

Prerequisites

ECON 100 and MATH 136 or MATH 151 or ECON 375

Credits

1 course

Spring Semester information

331A: Financial Mathematics

Professor: Zhixin Wu

Course Description

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.

Prerequisites

MATH 331 which may be taken concurrently.

Credits

1/2 course

Spring Semester information

332A: Seminar in Financial Math

Professor: Zhixin Wu

Course Description

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.

Prerequisites

Math 136 or MATH 151 or ECON 375, Econ 100, and either MATH 141 or ECON 350

Credits

1 course

Course Description

Topics in statistics.

Credits

1/4-1/2-1 course

Course Description

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

Science and Mathematics

Prerequisites

MATH 141 or ECON 350 or PSY 214 or BIO 275

Credits

1 course

Spring Semester information

341A: StatisticalModelAnalysis

Professor: Naima Shifa

Course Description

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

Science and Mathematics

Prerequisites

Math 141 (or ECON 350/BIO 375/PSY 214) and Math 151 (or MATH 135-136)

Credits

1 course

Spring Semester information

348A: Intro to Statistical Computing

Professor: Mamunur Rashid

Course Description

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

Prerequisites

MATH 152 and either MATH 223 or MATH 270

Credits

1 course

Fall Semester information

361A: Analysis

Professor: Sirous Homayouni

361B: Analysis

Professor: Sirous Homayouni

Course Description

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.

Prerequisites

MATH 152 and MATH 270

Credits

1 course

Spring Semester information

363A: Differential Equations

Professor: Sutthirut Charoenphon

Course Description

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.

Prerequisites

MATH 270 and CSC 121 or permission of instructor

Credits

1 course

Course Description

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

Prerequisites

MATH 270

Credits

1 course

Spring Semester information

371A: Algebraic Structures

Professor: Scott Hiatt

Course Description

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.

Prerequisites

MATH 270 or permission of instructor

Credits

1 course

Course Description

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

Credits

1/2 - 1

Winter Term information

390GA: AdvTps:Financial Risk Management with R

Professor: Zhixin Wu

Course Description

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.

Prerequisites

MATH 270

Credits

1 course

Course Description

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

Prerequisites

Math 422

Credits

1 course

Course Description

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.

Prerequisites

MATH 152 and MATH 223

Credits

1 course

Fall Semester information

441A: Probability

Professor: Zhixin Wu

Course Description

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.

Prerequisites

MATH 441 which may be taken concurrently

Credits

1/2 course credit

Fall Semester information

442A: ProbabilityProblmSeminar

Professor: Zhixin Wu

Course Description

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.

Prerequisites

Permission of instructor

Credits

1/2-1 course

Fall Semester information

490BA: Tps:Rings & Fields

Professor: Scott Hiatt

Course Description

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).

Prerequisites

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)

Credits

1 course

Spring Semester information

494A: Actuarial Science Case Studies

Professor: Zhixin Wu

Course Description

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

Credits

1 course

Spring Semester information

495A: Seminar

Professor: McKenzie Lamb,
Naima Shifa