# Mathematics and Statistics

## Department of Mathematics and Statistics

Website: www.washburn.edu/math

## Faculty

Associate Professor Sarah Cook, PhD Chair

Professor Mike Mosier, PhD

Professor Janet Sharp, PhD

Professor Jennifer Wagner, PhD

Associate Professor Gaspar Porta, PhD

Assistant Professor Guannan Hu, PhD

Lecturer Todd Cooksey, MA

Lecturer Angela Crumer, MS

Lecturer Stephanie Herbster, MS

Lecturer Beth McNamee, MA

Lecturer David Snyder, MA

## Mission

The mission of the Department of Mathematics and Statistics is to ensure all mathematics majors obtain a comprehensive knowledge of mathematics in terms of content, problem solving, analytical skills, and abstract mathematical reasoning. All mathematics majors will be able to communicate their skills and knowledge effectively and will be able to make appropriate choices regarding the method of solution and presentation of problems. We are committed to providing high-quality instruction at all levels, in our developmental, lower division, General Education, and upper-division courses. Further, the department is committed to providing service to the community and our profession in a variety of ways, including a number of on-campus programs for grade 6-16 learners, professional consultations, involvement in professional organizations, and other outreach activities.

## The Major

The Mathematics Department offers four specialties for mathematics majors. Note: Transfer students must complete at least nine upper division hours in mathematics from the Washburn Mathematics and Statistics Department.

## General Requirements

General requirements for the Bachelor of Arts degree or the Bachelor of Science degree are listed in the catalog. See pages listed in the index. Graphics calculators are required in all courses MA 112 Contemporary College Mathematics to MA 152 Calculus & Analytic Geometry II inclusive, and MA 253 Calculus/Analytic Geometry III.

**For a suggested initial schedule for all three specialties, please see your advisor.**

## Course Offerings

**MA 103** **Basic Algebra** **(3)**

A first course in algebra. Signed numbers and operations, integer exponents, linear equations and inequalities, lines, polynomials, factoring, rational expressions, applications involving linear equations. Does not count towards degree credit hour requirements, nor general education requirements. Prerequisite: None.

**MA 104** **Intermediate Algebra** **(3)**

Operations with polynomial and rational expressions, factoring, equations (linear, absolute value, quadratic, rational, root), inequalities (linear, compound, absolute value), graphing linear and quadratic functions, systems of linear equations, rational exponents and radicals, applications (involving linear, rational, and quadratic equations). This course is for student entering with one year of high school algebra who are preparing for Essential Mathematics or College Algebra. Does not count towards degree credit requirements, nor general education requirements. Students in this course are expected to have algebraic knowledge equivalent to MA 103 or one year of high school or junior high school algebra.

**MA 105** **Science Success Strategies** **(2)**

Interdisciplinary class may be taken as CH 100. Develops mathematics and science skills fundamental to science majors. Prerequisite: A grade of “C” or better in MA 104 (or equivalent) or an acceptable (as determined by the Mathematics Department) ACT mathematics score or SAT quantitative score or ACCUPLACER math score.

**MA 108** **College Algebra Preparation** **(3)**

This course is the first of a two-semester College Algebra sequence. Topics covered include: factoring, equations (linear, quadratic, rational, absolute value, root, linear systems), functions (notation, domain), graphing (linear, quadratic, piece-wise), inequalities (linear, compound, absolute value), applications involving linear, quadratic, and rational equations. Does not count towards degree credit requirements, nor general education requirements. Not open to students with credit in MA 112 or MA 116, or any MA-designated course numbered above MA 116. Students in this course are expected to have algebraic knowledge equivalent to MA 103 or one year of high school or junior high school algebra. Prerequisite: None.

**MA 112** **Contemporary College Mathematics** **(3)**

This course will focus on the mathematical skills and knowledge required for quantitative literacy, so the topics of understanding numerical relationships, financial mathematics, probability, and data analysis and statistics will be addressed. Each academic year the course will adopt a theme such as the political endeavor, the environment, art and culture and will study the topics from the context of the theme. The course will be project-based and to the extent possible the projects will investigate contemporary issues related to the overarching course theme. In addition to demonstrating mastery of the mathematical content, students will be expected to demonstrate an ability to understand how to determine the appropriate representation of quantitative information and to effectively communicate their assumptions and analysis. This course is not intended to prepare students for calculus. Graphics calculator required. Prerequisite: A grade of A or B in MA 090 or a grade of C or better in MA 104 or an ACT mathematics score of at least 22 or an equivalent background as determined by the Mathematics Department, for example, comparable SAT, COMPASS, or ACCUPLACER score.

**(General Ed Natural Science. Quan and Sci Reason Lit.)**

**MA 116** **College Algebra** **(3)**

Equations (linear system, polynomial, rational, absolute value, root, exponential, logarithmic), functions (notation, combining, domain, inverse), graphing (linear, quadratic, polynomial, piece-wise, rational, exponential, logarithmic), inequalities (compound, absolute value, polynomial, rational), logarithmic expressions, applications involving various types of equations and/or systems of equations. Not open to students with credit in MA 117, MA 123, or any course numbered above MA 140. Prerequisite: A grade of "C" or better in MA 104 (or equivalent) or a grade of "A" or "B" in MA 095 or an acceptable (as determined by the Mathematics Department) ACT mathematics score or SAT quantitative score or Compass or Accuplacer Mathematics Placement Test score.

**(General Ed Natural Science. Quan and Sci Reason Lit.)**

**MA 117** **Trigonometry** **(3)**

Trigonometric functions, their inverses, graphs, and identities. Solving trigonometric equations. A wide variety of applications, and appropriate use of technology. Graphics calculator required. Prerequisite: A grade of C or better in MA 116 or concurrent with MA 116 or an acceptable (as determined by the Mathematics Department) ACT mathematics score or SAT quantitative score or equivalent knowledge as determined by the Mathematics Department.

**(General Ed Natural Science. Quan and Sci Reason Lit.)**

**MA 123** **Pre-Calculus** **(3)**

Algebraic, exponential and trigonometric functions. Topics in plane analytic geometry. Designed for the student preparing for calculus. Not open to students with credit in MA 141 or MA 151. Prerequisite: A grade of “C” or better in MA 116 or MA 117 or an acceptable ACT mathematics score or SAT quantitative score or equivalent knowledge as determined by the Mathematics Department.

**(General Ed Natural Science. Quan and Sci Reason Lit.)**

**MA 131** **Topics in Trigonometry and Introduction to Calculus** **(3)**

Trigonometric functions, using right triangles and the unit circle. Trigonometric identities, sinusoidal graphs, and trigonometric applications, including periodic phenomena. Limits, continuity, rates of change, and the meanings of differentiation and integration. Not open to students with credit in MA 141 or MA 151. Prerequisites: MA 116 with a grade of "C" or better or an acceptable ACT mathematics score or SAT quantitative score or equivalent knowledge as determined by the Mathematics Department.

**(General Ed Natural Science. Quan and Sci Reason Lit.)**

**MA 140** **Statistics** **(3)**

Introduction to statistics and probability with practical applications. Descriptive techniques including graphical methods, linear regression, probability distributions, sampling distributions, confidence intervals, hypothesis tests. Graphics calculator required. Prerequisite: A grade of "C" or better in either MA 116 or MA 112 or, an acceptable ACT mathematics score or SAT quantitative score or Compass or Accuplacer Mathematics Placement score.

**(General Ed Natural Science. Quan and Sci Reason Lit.)**

**MA 141** **Applied Calculus I** **(3)**

Definition and elementary properties of the derivative and definite integral with emphasis on the application of the derivative and integral to problems in business. Not open to student with credit in MA 151. No more than five hours of credit will be awarded for MA 141 and/or MA 151. Prerequisite: A grade of “C” or better in MA 116 or MA 123 or an acceptable ACT mathematics score or SAT quantitative score or equivalent knowledge as determined by the Mathematics Department.

**(General Ed Natural Science. Quan and Sci Reason Lit.)**

**MA 142** **Applied Calculus II** **(3)**

A continuation of MA 141. Elementary differential and integral calculus including the trigonometric functions, techniques of integration and an introduction to multivariable calculus. Applications will be primarily from management and biological sciences. Not open to students with credit in MA 151. Prerequisites: A grade of “C” or better in MA 141 AND a grade of “C” or better in either MA 117 or MA 123 or consent of instructor.

**MA 145** **Mathematics for Decision Making** **(3)**

This course will introduce students to quantitative methods of decision making used in management, the life and social sciences. Topics covered will include: matrices, linear programming (including the simplex method), probability theory, Markov chains, graph theory, simulation and modeling. Prerequisite: A grade of “C” or better in MA 116 or MA 123 or an acceptable ACT mathematics score or SAT quantitative score or equivalent knowledge as determined by the Mathematics Department.

**MA 148** **Mathematics of Finance** **(3)**

**MA 151** **Calculus & Analytic Geometry I** **(5)**

Differential and integral calculus of the elementary functions with applications. No more than five hours of credit will be awarded for MA 141 and/or MA 151. Prerequisite: A grade of “C” or better in MA 117 or MA 123 or an acceptable ACT mathematics score or SAT quantitative score or equivalent knowledge as determined by the Mathematics Department.

**(General Ed Natural Science. Quan and Sci Reason Lit.)**

**MA 152** **Calculus & Analytic Geometry II** **(5)**

A continuation of Mathematics 151. Topics in plane analytical geometry, techniques of integration with applications, and infinite series. Graphics calculator required. Prerequisite: A grade of C or better in MA 151.

**MA 204** **Number Theory and Discrete Math for Middle School and Secondary Teachers** **(3)**

**MA 206** **Discrete Mathematics for Computing** **(3)**

Discrete mathematics topics useful in computer-aided problem solving. Topics will include Boolean algebra and computer logic, graphs and trees with algorithms, and analysis of algorithm complexity. Prerequisites: CM 111 and one of the following: A “C” or better in MA 116 or MA 123, or an acceptable (as determined by the Mathematics Department) ACT mathematics score or an acceptable SAT quantitative score, or equivalent knowledge as determined by the Mathematics Department.

**MA 207** **Discrete Mathematics** **(3)**

Logic, counting methods, induction, functions, equivalence, partial order, and congruence relations. Set up and solve recurrence relations problems. Graph theory and its applications. Significant emphasis on the format and method of mathematical proof. Prerequisite: MA 151 or MA 204 or MA 206, PH 110 or PH 220 or consent of instructor.

**MA 228** **Mathematics for Elementary and Middle School Educators I** **(4)**

The investigation of mathematical concepts and procedures encountered in grades K-8. Topics include rational numbers and operations, algebraic patterns, number theory, geometry, and measurement. Significant emphasis is placed on conceptual in-depth understanding of these mathematical topics and connecting those concepts to a range of procedures, as needed by beginning teachers. Prerequisite: A grade of "C" or better in MA 112 or higher, or, math ACT score or quantitative SAT score, or Compass Mathematics Placement score or equivalent knowledge as determined by the Mathematics Department.

**MA 229** **Mathematics for Elementary and Middle School Educators II** **(3)**

The investigation of mathematical concepts and procedures. Topics include Real numbers and operations, data analysis, measurement, introduction to non-Euclidean geometry, and introduction to probability. Significant emphasis is placed on conceptual in-depth understanding of these mathematical topics, connecting those concepts to a range of procedures and mathematics practices, applying the understandings within real world contexts and including appropriate use of technology. Prerequisites: MA 228 with a "C" or better.

**MA 230** **Mathematical Representations for Secondary Mathematics** **(4)**

Standard and non-standard algorithms of numbers (whole, integer, rational, and irrational) using multiple representations with a focus on linking concepts and procedures. Extend understandings to include ratio, rate, and proportions. Two and three-dimensional Euclidean geometry concepts including principles, shape-hierarchies, cross-sections, transformation, congruence, similarity, constructions, and proof. Extend understandings to formula derivation (perimeter, area, and volume) related to two- and three-dimensional objects. Represent abstract mathematical ideas encountered in grades 6-12 using multiple representations including concrete materials. Prerequisite: A grade of "C" or better in MA 116, or appropriate ACT/SAT quantitative score as determined by the Mathematics Department.

**MA 253** **Calculus/Analytic Geometry III** **(3)**

A continuation of Mathematics 152. Multivariable calculus, vectors in two and three-dimensional spaces. Graphics calculator required. Prerequisite: A grade of "C" or better in MA 152.

**MA 271** **Contemporary Actuarial Concepts** **(1)**

Current issues in Actuarial Mathematics with emphasis on the releases of the Society of Actuaries. Includes practical application to solving problems of the type included in the Society of Actuary’s Course P. Prerequisite: MA 253.

**MA 299** **Special Topics in Mathematics** **(1-6)**

Directed study in some area of mathematics at the lower division level.

**MA 301** **Linear Algebra** **(3)**

An introduction to the fundamental concepts and basic computational techniques of linear algebra. Topics investigated from both a theoretical and computational perspective include systems of linear equations, vector spaces, transformations, matrices, eigenvalues and eigenvectors, and orthogonality. Prerequisite: MA 152.

**MA 310** **Introduction to Operations Research** **(3)**

**MA 316** **Teaching Algebra** **(1)**

Pedagogical knowledge needed for teaching algebra. Emphasis on fundamental ideas of algebra including algebraic notation; interpreting the structure of an expression in terms of its context; function families and representations; and patterns of change. Includes co-teaching an algebra-based course. Prerequisites: A grade of "C" or better in MA 230 and in either MA 131 or MA 151.

**MA 317** **Teaching Trigonometry** **(1)**

Pedagogical knowledge needed for teaching trigonometry. Emphasis on fundamental ideas of trigonometry including right triangles, identities, application of periodic phenomena, and trig function families. Includes co-teaching a trigonometry-based course. Prerequisites: A grade of "C" or better in MA 230 and in either: MA 131 or MA 151.

**MA 318** **Teaching Statistics** **(1)**

Pedagogical knowledge needed for teaching statistics. Emphasis on fundamental ideas of statistics including variability, measures of central tendency, randomness, inference, and multiple representations. Includes co-teaching a statistics-based course. Prerequisites: C or better in MA 140 and in MA 230 and in either MA 131 or MA 151.

**MA 320** **Mathematics for Middle School Teachers** **(3)**

The investigation of mathematical problems as a means to develop as practitioners of the discipline of mathematics. Problems rely on a wide range of math topics. The primary focus of the course is on developing expertise in doing mathematics. By solving problems, students gain expertise in reasoning, constructing arguments, modeling, using resources, being precise, noticing deep structures of problems & expressing those structures with appropriate mathematical language. Significant emphasis on conceptual understanding of mathematics, connecting concepts to a range of realistic problem situations and appropriate use of technology. Understand and develop mathematical arguments and be able to clearly communicate those arguments using multiple representations. Prerequisite: MA 204 or MA 230 with a grade of "C" or better.

**MA 330** **Mathematical Models** **(3)**

Mathematical models will be constructed of real situations in biology, economics, social science, or engineering. The mathematical results of these models will be interpreted in the context of the real situation. Models utilizing graph theory are emphasized. Prerequisite: MA 207 or consent of instructor.

**MA 331** **Differential Equations** **(3)**

Methods for solving ordinary differential equations and systems of ordinary differential equations including Laplace transforms, series, numerical methods with applications. Prerequisite: MA 253 or concurrent.

**MA 340** **ANOVA/Design of Experiments** **(3)**

An introduction to the design and analysis of experiments, both single and multi-factor. Analysis of variance, both fixed effects and random effects. Topics will include Randomized Complete Block Design, the Latin Square Design, Incomplete Block Designs, Nested Designs, and the Split-Plot Design. Prerequisite: A 'C' or better in MA 140 Statistics.

**MA 341** **Nonparametric Tests/Quality Control** **(3)**

An introduction to nonparametric statistical procedures including signed-rank tests, sign tests, rank and rank sum tests, along with an introduction to the use of statistical methods for the purpose of quality control, including control charts for variables, control charts for attributes, the analysis of process capability, and acceptance sampling. Prerequisite: A "C" or better in MA 140 Statistics.

**MA 342** **Statistical Computing** **(3)**

An introduction to the statistical software packages SAS and R that includes basic commands and the structure, as well as data entry and manipulation, creating graphs and plots, simulation, bootstrapping, and introductory level programming. Prerequisite: A "C" or better in MA 140 Statistics.

**MA 343** **Applied Statistics** **(3)**

Sampling, concepts of experimental design. Tests of significance, point and interval estimation, simple and multiple regression, ANOVA, ANCOVA, non-parametric tests, logistic regression, and quality control. Emphasis on developing statistical thought, not just methodology, and on the use of computing technology. Prerequisite: MA 140 or equivalent, or consent of instructor.

**MA 344** **Mathematical Statistics I** **(3)**

**MA 345** **Mathematical Statistics II** **(3)**

An introduction to the theoretical framework of statistical methods including: point and interval estimators, large and small sample theories, hypothesis testing methods, linear statistical models with emphasis on repression and correlation, non-parametric testing methods, brief introduction to Bayesian methods for statistical inference. Prerequisite: MA 344.

**MA 346** **Regression Analysis** **(3)**

**MA 347** **Stochastic Processes** **(3)**

Generating functions, normal processes and covariance stationary processes, Poisson processes, renewal processes, Markov chains, discrete time processes. Prerequisite: MA 344.

**MA 348** **Time Series Analysis** **(3)**

**MA 349** **Statistical Topics for Actuarial Science** **(1)**

**MA 354** **Abstract Algebra** **(3)**

**MA 361** **Game Design** **(3)**

This course offers students the necessary background to design games on their own, including an introduction to the history of game design in the last 150 years. Students are then guided through an exploration of individual game mechanics which are frequently used in highly successful games. During these explorations the game mechanics are deconstructed to understand their structure using elementary mathematical tools, techniques, and language. While making these connections and observations, students are guided through isolated examples on how to integrate these into a game design. The course culminates with a final project in the form of an original game design of the students’ own making – either analogue (physical) or digital. Prerequisite: A grade of “C” or better in MA 112 or MA 116, or consent of instructor.

**MA 367** **Modern Geometry** **(3)**

This course will focus on the study of geometry as an axiomatic system. Emphasis will be placed on conjecture, proof and construction utilizing both classical tools as well as appropriate technology. Geometries investigated will include Euclidean, affine, projective, hyperbolic, and elliptical. A variety of approaches (synthetic, analytical and transformation) will be used to investigate the geometries. Prerequisite: MA 151.

**MA 371** **Introduction to Real Analysis I** **(3)**

**MA 372** **Introduction to Real Analysis II** **(3)**

Continuity, differentiation, the Riemann integral, sequences of functions, and infinite series. Prerequisite: MA 371.

**MA 373** **Applied Analysis** **(3)**

The algebra, geometry, and calculus of vectors. Fourier expansions, the Laplace transformation. Oriented toward applications in the physical sciences. Prerequisite: MA 253.

**MA 374** **Intro to Complex Variables** **(3)**

Theory of analytic functions, infinite series, Taylor and Laurent expansions. Prerequisite: MA 253.

**MA 376** **Numerical Analysis** **(3)**

Solution of algebraic and transcendental equations, numerical differentiation and integration, numerical methods in differential equations and linear algebra. Oriented toward machine computation. Prerequisites: MA 241 and CM 170.

**MA 380** **Problem Solving Strategies** **(1)**

Weekly problem sets require a wide variety of techniques to achieve solutions to the problems. Problem solutions may feature one or more techniques from calculus, linear algebra, discrete mathematics, statistics, geometry, and other areas. The course is repeatable up to three times. Prerequisite: A grade of "C" or better in MA 152, or consent of the instructor.

**MA 381** **History and Literature of Mathematics** **(3)**

Chronological development of mathematics, with emphasis on the great mathematicians of yore and periods of mathematical genius and invention. Topics include development of numeration systems, algebra, calculus, proof, Euclidean and non-Euclidean geometry, graphing technology, and philosophies of mathematics. Readings from extant and translations of mathematical text. Prerequisite: MA 151 or consent of instructor.

**MA 384** **Theory of Interest** **(3)**

Topics include measure of interest (emphasis on continuous nature), accumulated and present value factors, annuities, yield rates, sinking funds, and bonds and related securities. Prerequisite: MA 152 or concurrent.

**MA 385** **Actuarial Mathematics** **(3)**

**MA 388** **Capstone Research** **(1)**

Students must complete an individual semester project on a topic in the mathematical sciences under the guidance of one or more faculty from the department. The project serves as a culminating experience for Bachelor's degree students, requiring both a written and an oral component. A minimum of two hours of MA 380 Problem Solving Strategies are required unless permission is granted by the department Chair. Prerequisites: MA 151, MA 152, MA 253, MA 301, a minimum of two hours of MA 380; and, a total of 19 or more hours in mathematics/statistics (MA 151 or above), at least 6 hours of which must have been completed at Washburn University; and, consent of the instructor. Students must have junior or senior standing to enroll in this course.

**MA 390** **Seminar** **(1-3)**

Directed study in some advanced area. Prerequisite: Consent of instructor.

**MA 400** **Internship in Mathematics or Statistics** **(1-6)**

A work experience in the area of mathematics and/or statistics performed in cooperation with a business, industrial, medical or educational institution. The internship study must provide a learning experience in the applications of mathematics or statistics. Prerequisite: Consent of Department Chair.

**MA 450** **Topics in Mathematics** **(1-6)**

Directed study in some area of mathematics at the graduate level. Prerequisite: Consent of instructor.