## Faculty

Douglas R. Anderson, chair

Nathan D. Axvig

Daniel P. Biebighauser

Mark G. Causapin

Sarah E. Seger

Gregory M. Tanner

Julia C. Walk

The math department provides learning experiences that prepare students to achieve the following outcomes:

- demonstrate an understanding of a wide variety of fundamental mathematical concepts and the nature of mathematical proof
- read mathematical literature and communicate mathematical ideas effectively both orally and in writing, using appropriate language, good notation, and sound mathematical reasoning
- apply mathematical knowledge from one branch of mathematics to another as well as to other disciplines
- use appropriate technology
- have good problem-solving skills, including the ability to formulate problems, solve them and interpret solutions
- understand the historical and cultural framework of mathematics and the relationship of mathematics to other sciences and to the needs of society in general

In addition, teaching majors will be able to:

- gather, analyze and interpret data in an unbiased manner
- demonstrate that they know and can apply the national and state standards for mathematics instruction

The mathematics department sponsors an honors program for motivated students. An honors student must satisfy the following criteria:

- Maintain a GPA of at least 3.5 in mathematics courses.
- In each mathematics course the student takes after acceptance into the program, the student may be given one or more special assignment not expected of other students in the class (e.g., non-routine problems that might be too much for the typical student in the class).
- Complete a senior thesis under the guidance of some member of the department, based on an in-depth study or research project conducted with a department faculty member or at a Research Experience for Undergraduates (REU) program (or both). The senior thesis must be approved by the mathematics faculty.
- Give an oral presentation of the senior thesis to mathematics faculty and students on campus.
- Complete MATH 325 Modern Algebra I and MATH 330 Real Analysis I.

The student must submit a letter to the department chair applying to the honors program no later than the beginning of their second-to-last semester before graduation. The student must give a written proposal detailing their plans for a senior thesis no later than the end of the fourth week of their second-to-last semester. Both the oral presentation and the senior thesis must be completed no later than four weeks before the date of graduation – a paper or electronic copy of the thesis must be submitted to the chair of the department by this time. The department faculty will give decisions on the application to the program, the senior thesis proposal, and the final decision of whether or not to award honors promptly after each step in the process.

Students’ initial placement in mathematics courses is determined on the basis of their high school record. This list may be helpful:

- With one year algebra and one year of geometry or less, the recommended mathematics option is MATH 105 Exploring Mathematics.
- With algebra, geometry and higher algebra, options are:
Course List Code Title Hours MATH 105 Exploring Mathematics 4 MATH 110 Precalculus 4 MATH 203 Finite Mathematics 4 MATH 205 Introduction to Statistics 4 MATH 207 Discrete Mathematics 4 - With algebra, geometry and higher algebra senior math, options are:
Course List Code Title Hours MATH 121 Calculus I 4 MATH 203 Finite Mathematics 4 MATH 205 Introduction to Statistics 4 MATH 207 Discrete Mathematics 4

## Programs Offered

### Major

### Minor

### Mathematics Education

**Students seeking licensure to teach mathematics** must also fulfill the requirements for a major in education. For additional information about teaching mathematics, see the chair of mathematics or the chair of education.

## Courses

### Courses Offered during Alternate Years

#### 2021-22

- MATH 215 – Introduction to Probability and Statistics, 2 credits.
- MATH 220 – Introduction to Geometry Concepts, 2 credits.
- MATH 320 K – Geometry, 4 credits.
- MATH 328 – Complex Analysis, 4 credits.

#### 2022-23

- MATH 207 K – Discrete Mathematics, 4 credits.
- MATH 316, DATA 316 – Applied Statistical Models, 4 credits.
- MATH 330 – Real Analysis I, 4 credits.

### Course Descriptions

Numeration, number systems, geometry and other topics addressed in the elementary school curriculum. Required for students majoring in elementary education.

**Frequency:**

*Every Semester*

This course uses real-world problems and situations to improve students' problem-solving skills, to improve their ability to apply mathematics, and to enhance their appreciation of the importance of mathematics in our modern world. Topics will be chosen from voting theory, number theory, taxicab geometry, graph theory, probability, statistics, and financial mathematics. This course can be used to fulfill the math exploration requirement.

**Frequency:**

*Every Semester*

**Core designations:**Mathematics K

A study of the function concept and properties of the polynomial, exponential, logarithmic and trigonometric functions. Prerequisites: high school geometry and higher algebra

**Frequency:**

*Every Semester*

**Core designations:**Mathematics K

An introduction to the concepts of limits, continuity, derivatives and antiderivatives and their applications, and an introduction to the Riemann integral and integration techniques, including by substitution. Some review of trigonometry and analytic geometry is included.

**Frequency:**

*Every Semester*

**Core designations:**Mathematics K

Applications of the definite integral, techniques of integration, parametric equations, introduction to differential equations, sequences, series and Taylor and Maclaurin Series.

**Frequency:**

*Every Semester*

**Prerequisites:**MATH 121

**Core designations:**Mathematics K

The course examines combinatorics, probability, descriptive and inferential statistics, linear programming, and mathematics of finance. Prerequisite: high school higher algebra

**Frequency:**

*Every Semester*

**Core designations:**Mathematics K

This is an introductory course in statistical methods for science and mathematics students. The object of this course is to provide students with a conceptual introduction to the field of statistics, including the determination of the appropriate procedures for data analysis and the proper interpretation of results. Statistical significance and confidence intervals will be explored, along with statistical modeling through regression, ANOVA, and chi-squared techniques. The theory will be illustrated by examples from the life, health, and social sciences. Prerequisite: high school higher algebra. This course can also count toward the environmental and sustainability studies program.

**Frequency:**

*Every Semester*

**Core designations:**Mathematics K

Logic, sets, functions, sequences and series, matrices, algorithms, methods of proof, combinatorics, recurrence relations, linear programming, graphs and trees. A previous mathematics class at or above MATH 110 - Precalculus (or the equivalent) is highly recommended.

**Frequency:**

*Alternate Years - 2nd Semester*

**Core designations:**Mathematics K

Vectors, matrix algebra, systems of linear equations, determinants, vector spaces, span and basis, eigenvalues and eigenvectors. Also includes an introduction to proof.

**Frequency:**

*Every Semester*

**Prerequisites:**MATH 122

Basic concepts of data analysis, randomness and uncertainty required for elementary mathematics specialization. Topics include: data collection, exploratory data analysis, measures of central tendency and spread, theoretical probabilities in simple and compound events, basics of experimental design, and evaluating predictions and arguments from data.

**Frequency:**

*Alternate Years - 2nd Semester*

Basic geometry content for students seeking elementary mathematics specialization. Topics will include: deriving and describing shapes, characteristics of geometric objects, spatial reasoning with geometric models, elementary geometric transformations, analysis and presentation of geometric arguments, and measurement and estimation.

**Frequency:**

*Alternate Years - 2nd Semester*

**Prerequisites:**MATH 102

Multivariable calculus and applications, line integrals, surface integrals. Green's Theorem, Stoke's Theorem and the Divergence Theorem.

**Frequency:**

*Every Semester*

**Prerequisites:**MATH 122

**Core designations:**Mathematics K

An introduction to the art and science of mathematics, the axiomatic system that forms its foundation, the historical factors that have influenced its development, its close ties to astronomy, the sciences, art and religion; and its role in the development of Western culture.

**Frequency:**

*Not offered on a Regular Basis*

**Prerequisites:**MATH 250

**Core designations:**International-Global Prspct G

Differential equations and models, analytic and qualitative solutions, nth-order equations, linear systems, harmonic oscillators, Laplace transforms, initial and boundary value problems, bifurcation.

**Frequency:**

*Every Year - Second Semester*

**Prerequisites:**MATH 122

**Core designations:**Mathematics K

An introduction to Fourier and other methods for solving partial differential equations, including the heat, wave and potential equations and related boundary value problems.

**Frequency:**

*Not offered on a Regular Basis*

Introduction to the basic concepts in probability theory, including discrete and continuous probability functions, independence, random variables, order statistics, expected value, variance and moment generating functions. Specific attention given to normal, Poisson and geometric distributions, as well as estimation and estimators.

**Frequency:**

*Every Year - First Semester*

**Prerequisites:**MATH 223

An introduction to the construction and analysis of least-squares models, including multiple regression, ANOVA, ANCOVA, and mixed models. Generalized linear models will also be presented, with special attention paid to logistic regression and log-linear models. Examples and applications will be drawn from various disciplines, including biology, medicine, economics, engineering, and the social sciences.

**Frequency:**

*Alternate Years - 2nd Semester*

Euclidean, non-Euclidean, projective and other geometries as time permits.

**Frequency:**

*Alternate Years - 2nd Semester*

**Prerequisites:**MATH 210

**Core designations:**Mathematics K

Introduction to basic algebraic systems: groups, rings, integral domains and fields. Special attention is given to the ring of integers.

**Frequency:**

*Every Year - First Semester*

**Prerequisites:**MATH 210

The algebra and geometry of complex numbers, elementary analytic functions, complex functions defined by power series, differentiation and integration of complex functions with selected applications.

**Frequency:**

*Alternate Years - 2nd Semester*

**Prerequisites:**MATH 223

A proof-based course that covers-sets, real numbers, sequences and convergence, limits of functions, continuity and differentiability, the Riemann integral, infinite series, and sequences and series of functions.

**Frequency:**

*Alternate Years - 2nd Semester*

An introduction to the theory and practice of quantitative modeling and optimization, with applications to computer simulation and business resource management. Possible topics include linear and nonlinear programming, network analysis, game theory, deterministic and probabilistic models.

**Frequency:**

*Every Year - First Semester*

**Corequisites:**PEAK 400

**Core designations:**Mathematics K

Courses covering various topics of interest in this particular discipline are offered regularly. Contact department or program chair for more information.

**Frequency:**

*Not offered on a Regular Basis*

**Repeatable:**Yes

Required of all senior Group 2 mathematics majors (mathematics and education double majors seeking reaching licensure). Topics in mathematics history are discussed using the seminar format. With the guidance of faculty members, each student researches a topic and delivers an oral presentation on that topic. Prerequisite: senior standing in both mathematics and education, or permission of instructor.

**Frequency:**

*Every Year - Second Semester*

Further study of the basic algebraic systems introduced in MATH 325 - Modern Algebra I.

**Frequency:**

*Not offered on a Regular Basis*

**Prerequisites:**MATH 325

Further study of topics listed under MATH 330 - Real Analysis I.

**Frequency:**

*Not offered on a Regular Basis*

**Prerequisites:**MATH 330

This course provides an opportunity for individual students to conduct in-depth study of a particular topic under the supervision of a faculty member. A seminar on non-routine problems sometimes is conducted. Prerequisite: Consent of faculty. Contact the department or program chair for more information.

**Frequency:**

*Every Semester*

**Repeatable:**Yes

This course provides an opportunity for individual students to conduct research in a specific area of study, completed under the direction of a faculty mentor. Specific expectations of the research experience to be determined by the faculty. Repeatable for credit. Prerequisite: consent of instructor.

**Frequency:**

*Not offered on a Regular Basis*

**Repeatable:**Yes