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 

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 onehalf 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 201314 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 
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 340, MATH 441, MATH 423, ECON 450. 
Number 300 and 400 level courses  2 
Courses in Mathematics
MATH 123Computational 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, chisquared, studentt and F. Students who have completed or are concurrently enrolled in ECON 350 will only receive onehalf 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 problemsolving 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 twosemester 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, higherorder 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
FirstYear 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 decisionmaking 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 singlevariable 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 momentgenerating functions, Gamma distributions, Chisquared distributions, tdistributions, and Fdistributions, 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, nonEuclidean 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 NoArbitrage Principle; basics of fixedincome instrument and riskfree asset; Riskneutral Probability and RiskNeutral Pricing; BlackScholes' 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 

1/41/21 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 modelsmethod 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 Ftests and sequential Ftests. 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 135136).
Distribution Area  Prerequisites  Credits 

Science and Mathematics  Math 141 (or ECON 350/BIO 375/PSY 214) and Math 151 (or MATH 135136)  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, boundaryvalue problems and nonlinear 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 highlevel language. Prerequisites: MATH 270 and CSC 121
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, numbertheoretic 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  1/21 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 