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Course Catalog

Mathematics

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

Actuaries are responsible for determining rates and premiums on insurance policies (e.g. life, health, home and auto) and forecasting future events affecting the soundness of insurance programs. Some actuaries work with consulting firms as advisors to corporations regarding human resource and pension benefits. Government agencies, such as the Social Security Administration or insurance regulatory boards, also employ actuaries. Actuaries can specialize in life and health insurance, in property and casualty insurance, or in pension benefit programs. The department of mathematics encourages the development of skills in analytical thinking and problem solving that prepare our students for life beyond DePauw. Actuarial Science is a collection of mathematical and statistical techniques that make it possible to calculate the monetary value of uncertain future events. Actuaries apply these principles and techniques to solve problems in finance, insurance and related fields. Actuaries are involved with every aspect of the insurance industry and must possess strong mathematical skills and a solid business background to apply their technical knowledge.


Requirements for a major

Actuarial Science

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, ECON 393 or ECON 450
Number 300 and 400 level courses Five
Senior requirement and capstone experience The senior requirement consists of 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 This new major will become available in the 2013-14 academic year.
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 442.
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

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 Mathematics

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.

Distribution Area Prerequisites Credits
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 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 135 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 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 136 or MATH 151 or permission of instructor.

Distribution Area Prerequisites Credits
MATH 136 OR MATH 151 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 341

Statistical Model Analysis

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 tables, 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. Pre-requisite: 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 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 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 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