# Mathematics Courses

## 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

### Mathematics of Compound Interest

A mathematical treatment of measurements of interest and discount, present values, equations of value, annuities, amortization and sinking funds and bonds. Also, an introduction to life annuities and the mathematics of life insurance. *Prerequisite: MATH 152 or permission of instructor.*

Distribution Area | Prerequisites | Credits |
---|---|---|

MATH 152 | 1 course |

MATH 332

### Seminar in Financial Mathematics

This is a problem solving seminar that looks at the application of general derivatives, options, hedging and investment strategies, forwards and futures, and swaps. The context of these topics is actuarial science and financial mathematics. This course is of great assistance for students who are preparing for the actuarial exam (FM). * Prerequisite: MATH 331 which may be taken concurrently.*

Distribution Area | Prerequisites | Credits |
---|---|---|

MATH 331 which may be taken concurrently. | .5 course |

MATH 336

### An Introduction to Financial Engineering

The course builds on mathematical models of bond and stock prices and focuses on the mathematical modeling of financial derivatives. It covers several major areas of financial derivative pricing modeling, namely: Efficient market and No-Arbitrage Principle; basics of fixed-income instrument and risk-free asset; Risk-neutral Probability and Risk-Neutral Pricing; Black-Scholes' arbitrage pricing of options and other derivative securities; Numerical Methods like a Binomial Tree for derivative pricing; the Greeks and Hedging using derivatives. Assuming only a basic knowledge of probability and calculus, it covers the material in a mathematically rigorous and complete way at a level accessible to second or third year undergraduate students. This course is suitable not only for students of mathematics, but also students of business management, finance and economics, and anyone with an interest in finance who needs to understand the underlying theory. * Prerequisites: MATH 136 or MATH 151, ECON 100, and either MATH 141 or ECON 350.*

Distribution Area | Prerequisites | Credits |
---|---|---|

Math 136 or MATH 151, 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 Science Case Studies

This course is primarily based on lectures and group discussions. Students participating in this senior capstone course are exposed to case studies in Actuarial Science and Financial Mathematics. Students will work in groups to complete various projects such as mortality and lapse studies in insurance and use public data in the Society of Actuaries, Casualty Actuarial Society, and other resources to model and price financial derivatives. Students will apply techniques from previous courses to real-world data using data analytic methods and tools to complete research. *The prerequisites of this course are two core actuarial science courses (Math 331 Theory of Compound Interest or Math 336/Econ 390 Introduction to Financial Engineering, and Math 441 Probability) plus one upper-level statistics course offered in the Math Department (Math 341 Statistics Model Analysis, Math 348 Introduction to Statistical Computing) or Econ department (Econ 385 Regression and Simulation for Economics and Management, Econ 450 Econometrics).*

Distribution Area | Prerequisites | Credits |
---|---|---|

MATH 331 or MATH 336/ECON 390 and MATH 441 plus MATH 341, MATH 348, ECON 385 or ECON 450 | 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 |