# Mathematics

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# Mathematics Overview & Goals

Mathematics is a discipline that simultaneously offers an excellent supplement to other programs while remaining a rich field of study in its own right. The critical-thinking, problem-solving, and quantitative-reasoning skills learned here serve Bethanians well as productive members of the world in which they immerse themselves upon graduation.

In addition to a solid understanding in the foundations of computational and proof-based mathematics, our major provides a strong opportunity for students to apply their skills to actuarial sciences, computer science, economics, physics, and pure mathematics.

There are numerous research, presentation, and internship opportunities available to a Bethany mathematics major. A minor in mathematics and a dual major with economics are additional options for the interested student in other fields. Our graduates have successfully found homes in financial institutions, engineering, information solutions, and postgraduate research.

## Areas Of Study

## CAREERS IN Mathematics

- Mathematician
- Actuary
- Statistical analysis
- Market research
- Survey research
- Financial advisor

- Cost estimator
- Real estate appraiser
- Operations research analyst
- Logistics
- Supply chain management

## REQUIREMENTS MATHEMATICS MAJOR

The student is required to take the following core courses: MATH 106, 201, 202, 203, 220, 354, 373, 400, 403, 477, 495 and either MATH 326 or 410; a senior project. In addition, each student must complete one of the following tracks:

**Mathematics:** CPSC 151; a minimum of 12 credits from the following: MATH 210, 310, 326, 341, 383, 384, 390, 410; CPSC 152.

**Mathematics-Actuarial Science:** MATH 210, 341, 383, 384, 390; CPSC 151.

**Mathematics-Computer Science:** CPSC 151, 152, 275, 390; MATH or CPSC 210.

**Mathematics-Economics:** MATH 210, 383, 384; ACCT 202; ECON 162, 163, 301, 302; CPSC 151.

**Mathematics-Physics:** MATH 341; PHYS 201, 202, 251 or 261, 300; CPSC 151.

## REQUIREMENTS MATHEMATICS MINOR

## COURSE DESCRIPTIONS MATHEMATICS

**MATH 103 College Algebra 3 credits**

The course examines sets and operations on sets, numbers systems, algebraic expressions, exponents, solutions to equations, inequalities, and graphing. (Not open to students who have credit for a Level IV mathematics course or its equivalent, or to students with a Level III or Level IV mathematics placement score.)

**MATH 103X College Algebra Support 2 credits**

This course provide foundational and supportive mathematics instruction for college students. Emphasis is placed upon conceptual understanding of mathematics with corresponding computational skill development.

**MATH 105 Precalculus 3 credits**

This course examines functions, including linear, quadratic, exponential, logarithmic, and trigonometric functions. (Not open to students who have credit for a Level IV mathematics course or its equivalent, or to students with a Level IV mathematics placement score.) Prerequisite: Level III mathematics placement, or successful completion of a Level II course.

**MATH 106 Introduction to Mathematica 2 credits**

This course introduces the student to the use of the computer program Mathematica. Students majoring in mathematics are expected to take this course in their first year so that Mathematica may be employed in all subsequent courses.

**MATH 120 Foundations of College Mathematics 3 credits**

This course represents Level IV mathematics placement. Successful completion of MATH 120 bars students from credit for any lower numbered mathematics course with the exception of MATH 106.

**MATH 170 Connections in Mathematical Understanding 3 credits**

This course examines the connections between mathematics and other liberal arts disciplines. Topics for discussion include mathematics in language, philosophy, art of symmetry, perspective, mathematics in movies and literature, daily applications of mathematics, the application of statistics, and practical uses of geometry.

**MATH 201 Calculus I 4 credits**

This course is a study of the real number system, equations of a line, functions, limits, and continuity, and of techniques of differentiation and integration applied to maximum and minimum problems and to related rates. (The course includes four hours of class and one laboratory session each week.) Prerequisites: Level IV mathematics placement; successful completion of a Level III mathematics course or equivalent; or permission of the instructor.

**MATH 202 Calculus II 4 credits**

This course focuses on integration and differentiation of log, exponential, trig, and inverse functions. Additional topics include methods of integration, integration by parts, partial fractions, trigonometric substitution, L’Hôpital’s rule, sequences, and series. Prerequisite: MATH 201 or the equivalent.

**MATH 203 Calculus III 4 credits**

This course is a study of the calculus of functions of several variables and of vector valued functions. Topics include vectors, partial differentiation and integration, multiple integrals, line and surface integrals, and theorems of vector calculus. Prerequisite: MATH 202.

**MATH 210 Discrete Mathematics 3 credits**

This course introduces the student to the fundamental concepts of mathematics involved in computer science. Topics include induction, elementary counting, combinations and permutations, recursions and recurrence relations, graphs and trees, sorting and searching, and Boolean algebra. (This course may be taken for credit as CPSC 210.) Prerequisite: Level III mathematics placement, or successful completion of a Level II mathematics course.

**MATH 220 Introduction to Proofs and Abstract Thinking 2 credits**

This course reviews the fundamental concepts of sets, relations, and functions while developing the mathematical writing, reading, and understanding of formal proofs covering topics in mathematics.

**MATH 241 Mathematical Methods in the Physical Sciences 3 credits**

This course is primarily intended for students with one year of calculus who want to develop, in a short time, a basic competence in each of the many areas of mathematics needed in junior to senior courses in physics and chemistry. Thus, it is intended to be accessible to sophomores (or freshmen with AP calculus from high school). Topics include ordinary and partial differential equations, vector analysis, Fourier series, complex numbers, eigenvalue problems, and orthogonal functions. (This course may be taken for credit as PHYS 241.) Prerequisites: MATH 201, 202 or permission of the Instructor.

**MATH 250 Mathematics for Elementary Education 3 credits**

This is a course designed in content and teaching style for elementary pre-service teachers. The course emphasizes active student participation and a field placement component which permits students to develop materials and evaluation instruments and to practice the teaching of mathematics concepts, including the structure of number systems, real number properties and the computation derived from them, problem solving strategies, and geometry and measurement. Prerequisite: Level III mathematics placement, or successful completion of a Level II mathematics course. Not open to freshmen.

**MATH 252 Mathematics for Teachers: Algebra and Geometry 3 credits**

This is a sophomore or junior level course designed in content and teaching style for pre-service teachers of the middle and secondary grades. The NCTM Mathematics Curriculum and Evaluation Standards are incorporated in all phases of the course. The course emphasizes active student involvement and the use of a variety of software programs. Course content includes topics found in the middle and secondary grades (basic algebra and geometry), as well as the expansion of these topics as they are encountered through the grades. Particular attention is placed on the identification of objectives for each concept and the particular NCTM Standards as they are encountered at specific grade levels. Prerequisite: MATH 250 or permission from the department.

**MATH 278 Mathematics for Standardized Testing 1 credit**

This activity course serves as a problem-solving session for those students interested in sitting for and succeeding on standardized exams with mathematical skill sections.

**MATH 281 Statistical Methods I 3 credits**

This course is an introduction to statistical analysis including frequency distributions and graphic presentation of data, measures of central tendency, measures of dispersion, probability, the normal curve and its applications, confidence intervals, testing hypotheses, correlation, and regression. Not open to students with credit for MATH 383.

**MATH 281X Statistical Methods Support 2 credits**

This course provide foundational and supportive mathematics instruction for college students. Emphasis is placed upon conceptual understanding of mathematics with corresponding computational skill development.

**MATH 282 Statistical Methods II 3 credits**

This course is a study of analysis of variance, multiple regression, non-parametric methods, time series, index numbers, and decision analysis. Prerequisite: MATH 281 or equivalent. Not open to students with credit for MATH 384.

**MATH 310 Number Theory 3 credits**

This course examines properties of the integers including prime numbers and their distribution, the Euclidean algorithm, linear and nonlinear Diophantine equations, congruences, multiplicative functions, primitive roots, continued fractions and quadratic residues. Applications of number theory to such areas as computer science, cryptography, and networks are studied. Software technology such as Mathematica, Matlab, or Maple is also used to examine number theoretic properties and their applications.

**MATH 326 Introduction to Modern Geometry 4 credits**

This course is an introduction to Euclidean and non-Euclidean geometries and synthetic projective geometry, the concept of limit and infinity, geometrical constructions, and recent developments and theorems. Prerequisite: MATH 202 or permission of the instructor.

**MATH 341 Differential Equations 3 credits**

This course is a study of the methods of solution of ordinary and partial differential equations and of applications of differential equations. Prerequisite: MATH 202.

**MATH 354 Linear Algebra 3 credits**

This course is a study of geometric vectors, matrices and linear equations, real vector spaces, linear transformations and matrices, and inner product spaces. Prerequisite: MATH 202 or equivalent.

**MATH 373 Writing for Mathematics and Computer Science 2 credits**

This course is designed to introduce the process of presenting solutions to mathematical problems, proofs to mathematical theorems, and preparing and presenting research papers in the mathematical sciences. (This course may also be taken for credit as CPSC 373.)

**MATH 383 Probability & Statistics I 3 credits**

This course is an introduction to probability, basic distribution theory, mathematical expectations, probability densities, and random variables. Prerequisite: MATH 202 or permission of the instructor.

MATH 384 Probability and Statistics II 3 credits

This course is a study of sampling distributions, point and interval estimation, tests of hypotheses, regression and correlation, and analysis of variance. Prerequisite: MATH 383.

**MATH 390 Numerical Analysis 3 credits**

This course is a study of numerical methods in evaluating integrals and differential equations, techniques in finding the roots of polynomials, solving systems of linear equations, and matrix manipulation. (This course may be taken for credit as CPSC 390.) Prerequisites: MATH 202 or equivalent; CPSC 151.

**MATH 400 Abstract Algebra 4 credits**

This course is a study of groups, rings, integral domains, fields, and vector spaces. Prerequisite: MATH 220.

**MATH 403 Introduction to Real Analysis 4 credits**

This course concentrates on the careful study of the principles underlying the calculus of real valued functions of real variables. Topics include sets and functions, compactness, connectedness, uniform convergence, differentiation, and integration. Prerequisites: MATH 203, 220.

**MATH 410 Topology 3 credits**

This course is a study of those properties of objects that are preserved when stretching, twisting, bending, or compressing an object without tearing it and without identifying any two of its points. Topics include metric and topological spaces, cardinality, countability properties, separation axioms, continuity, and homeomorphic spaces. Prerequisite: MATH 202,220.

**MATH 420 Professional Internship 1-8 credits**

This course is a professionally supervised experience with off-campus mathematicians, computer scientists, or applied scientists using modern research and/or analytical techniques. Settings may vary from purely academic summer programs to private or public scientific institutions. The number of credits awarded depends on the number of imbedded hours in the internship experience. A minimum of 50 imbedded hours is expected per credit with the maximum number of credit earned is eight. Prerequisites: Students must have a cumulative 2.0 GPA and junior/senior standing.

**MATH 430 History of Mathematics 2 credits**

This course is an exploration of the origins and development of mathematics including the philosophy of the mathematical sciences. Mathematical theories and techniques of each period and their historical evolution are examined.

**MATH 477 Seminar in Mathematics and Computer Science 2 credits**

This course includes topics in mathematics suitable to math majors. The course is open to qualified junior and senior math majors. (This course may be taken for credit as CPSC 477.)

**MATH 479 Mathematics for Competition 1 credit**

This activity course serves as a problem-solving session for those students interested in actively participating in competition-level mathematics.

**MATH 480 Methods and Materials in Teaching Mathematics 3 credits**

This course is a study of the approved methods in teaching mathematics at the middle and secondary level. The emphasis is on the following: class period activities of the teacher; procedures and devices in teaching; organization of materials; testing aims; modern trends. (This course may be taken for credit as EDUC 480. A 30 hour field placement is required.) Prerequisites: EDUC 242; a passing score on PRAXIS I Core Academic Skills for Educators; admission to the teacher education program.

**MATH 487-488 Independent Study 2-4 credits**

**MATH 490 Senior Project 2-4 credits**

**MATH 495 Comprehensive Exams**

This course is an administrative placeholder used to record a student’s score on Comprehensive Exams (CR/NCR).

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