## Program Highlights

The secondary mathematics education program is an Illinois State Board of Education Approved Program for the Preparation of Educational Personnel in Illinois Institutions of Higher Education. Students interested in teacher certification should elect this option.

In addition to the foundation requirements, students must take

- MA301 - College Geometry
- MA320 - History of Mathematics
- MA403 - Abstract Algebra
- MA425 -Methods of Teaching Mathematics in Grades 6 through 12
- MA471 - Internship in Methods of Teaching Mathematics
- Two courses selected from:
- MA305 - Differential Equations
- MA313 - Numerical Analysis
- MA314 - Advanced Mathematical Statistics
- MA340 - Calculus III
- MA420 - Mathematical Logic
- MA440 - Advanced Calculus
- MA491,492,493,494 - Independent Study

Teacher certification in the State of Illinois mandates students earn a C or better in all required mathematics and education courses. Teacher certification also requires specific coursework in education and other areas. See the School of Education section for details. Students should consider preparation in a second teaching field to increase the breadth of their knowledge and the probability of finding a teaching position upon graduation.

### Plans of Study

## Departmental Course Offerings

Courses change each semester, so this list should not be considered a commitment to these individual topics. However, this does represent a list of many of our current and popular courses. The list is provided so that you can begin to imagine your academic career at Millikin in this major.

Basic Mathematics | Basic principles of arithmetic: integers, fractions, decimals, ratios, proportions, measurement, percent, descriptive graphs, and basic statistics. Will not satisfy quantitative reasoning requirements of MPSL. A student who has passed a quantitative reasoning course or has previously earned a placement score of 3 or higher may not receive credit for any of MA087, MA091, or MA098. Prerequisite: Course open only to first-year students with ACT mathematics subscore below 17. (MA087) |
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Basic Algebra | Concepts and techniques of basic algebra with applications. Includes review of arithmetic of real numbers, linear equations and inequalities, polynomials and arithmetic operations on polynomials, factoring, rational expressions and equations, graphs and an introduction into functions. Will not satisfy quantitative reasoning requirements of MPSL. A student who has passed a quantitative reasoning course or has previously earned a placement score of 3 or higher may not receive credit for any of MA087, MA091, or MA098. Prerequisite: ACT mathematics subscore of 17 or 18, a placement score of 1, or a pass in MA087. (MA091) |

Intermediate Algebra | Further study of algebra concepts and techniques with applications. Includes functions and graphs, systems of equations, systems of linear inequalities, radical functions and equations, complex numbers, quadratic functions, exponential and logarithmic functions, and conic sections. Will not satisfy quantitative reasoning requirements of the MPSL. A student who has passed a quantitative reasoning course or has previously earned a placement score of 3 or higher may not receive credit for any of MA087, MA091, or MA098. Prerequisite: ACT mathematics subscore of 19,20, or 21, placement score of 2, or a pass in MA091. (MA098) |

Finite Mathematics | Analysis, description and solution of problems arising in business, computer science, and natural and social sciences. Emphasis on mathematical models whose construction and solution involve a finite number of clearly defined steps. Includes an introduction to finite probability and elementary statistics. Topics include matrices, systems of linear equations, linear inequalities, linear programming, functions and their graphs, Markov processes, and game theory. Additional topics may be selected from decision theory, mathematics of finance and networking. Prerequisite: ACT mathematics subscore of 22 or higher, a placement score of at least 3, or a pass in MA098. (MA109) |

College Algebra | Study of basic operations: equations and inequalities, polynomial, exponential, and logarithmic functions and graphs, matrices, determinants, sequences, series, mathematical induction, and selected topics from combinatorics. Prerequisite: ACT mathematics subscore of 22 or higher, placement score of at least 3, or a pass in MA098. (MA110) |

Math Content for Elementary Teachers I | Designed to help prepare a prospective elementary school teacher in mathematics. Includes a study, from a problem-solving standpoint, of many topics covered in elementary school mathematics such as natural numbers, whole numbers, rational and irrational numbers, arithmetic operations on these numbers, systems of numeration, language and nature of inductive and deductive reasoning, elements of set theory, informal geometry and elementary number theory. Prerequisite: Elementary of early childhood major or consent of instructor; and ACT mathematics subscore of 25 or higher. a placement score of at least 4, or a pass in MA098. (MA112) |

Math Content for Elementary Teachers II | This second course is designed to help further prepare a prospective elementary school teacher in mathematics. It includes a study, from a problem-solving standpoint, of many topics covered in elementary school mathematics such as geometry, measurement, probability and statistics. Pre-requisites: Elementary of early childhood major or consent of instructor; and ACT mathematics subscore of 25 or higher. a placement score of at least 4, or a grade of C or better in MA110. (MA113) |

Trigonometry | Study of thew trigonometric functions and their properties, applications to triangles and other geometric figures, and also graphs of trigonometric functions and inverse trigonometric functions. Prerequisite: ACT mathematics subscore 25 or higher.a placement score of at least 4, or a C- or better in MA110. (MA115) |

Elementary Probability and Statistics | Introduction to descriptive statistics, relevant concepts in probability including random variables and their distributions, sampling, inferential statistics and regression. Applications to several disciplines. Prerequisite: ACT mathematics subscore of 25 or higher, placement score of at least 4, or grade of C- or better in either MA109 or MA110. (MA120) |

Elementary Probability and Statistics with Spreadsheets | Introduction to descriptive statistics, relevant concepts in probability (including random variables and their distributions), sampling, inferential statistics, hypothesis testing, and regression. Applications to business are emphasized, and spreadsheets are used as an analytical tool. (MA130) |

Calculus I | Differential and integral calculus of the elementary functions with associated analytic geometry; concepts of limit, continuity, derivative and integral; applications of the derivative as rate of change, slope and solving max-min problems. Prerequisite: Successful completion of calculus readiness exam, or a grade of C- or better in MA115. (MA140) |

Discrete Mathematics | Introduces basic techniques of proof and combinatorial problem solving. Topics include graphs, trees, logic, applied combinatorics, and number theory. Prerequisite: Completion of or concurrent enrollment in MA140. (MA208) |

Intro to Actuarial Science | Topics will include probability, risk theory, financial mathematics and basic accounting as used by actuaries in insurance companies. This course is one component in the preparation of actuarial students for internships with insurance companies. Prerequisite: ACT mathematics subscore of 25 or higher, placement score of at least 4, or grade of C- or better in either MA109 or MA110, or consent of instructor. (MA215) |

Statistical Methods | Introduction to major methods of applied statistics. Topics may include simple and multiple regression, analysis of variance and co- variance, model specification and residual analysis, nonparametric inference, experimental design, survey sampling, multivariate analysis and Bayesian inference. Prerequisite: a grade of C- or better in MA120. (MA220) |

Time Series | Introduction to modeling time series data using smoothing techniques, regression, and autoregressive models. Estimation, data analysis and forecasting using real data will be examined. Prerequisite: MA 220. (MA225) |

Calculus II | Applications of definite integral and Fundamental Theorem of Calculus, methods of integration, integrals of inverse trigonometric functions, logarithmic and exponential functions, the use of polar coordinates, infinite series, power series, Taylor series and Fourier series. Prerequisite: a grade of C- or better in MA140. (MA240) |

College Geometry | Elements of plane and solid geometry treated from both a synthetic and metric approach, historical development of geometry, parallelism and symmetry, area and volume, other geometrics including hyperbolic non-Euclidean geometry, projective geometry and finite geometries. Prerequisite: a grade of C- or better in MA140. (MA301) |

Linear Algebra | Matrices, linear systems, finite dimensional vector spaces, vector geometry, linear transformations, quadratic forms. Prerequisite: a grade of C- or better in MA240.Completion of MA208 recommended. (MA303) |

Probability and Mathematical Statistics | Combinatorial analysis, probability axioms, random variables and their distributions including binomial, normal, Student's t and f, estimation and sampling, hypothesis testing, linear and multivariate regression. Prerequisite: a grade of C- or better in MA240. (MA304) |

Differential Equations | Elementary differential equations and applications including linear differential equations with constant coefficients and first order systems, higher order differential equations and applications. Existence and uniqueness theorems. Numerical techniques. Prerequisite: Mathematics 340 and concurrent enrollment or completion of MA303. (MA305) |

Theory of Computation | An introduction to the theory of computation emphasized formal languages, automata, and computability. Includes computational complexity and NP-completeness. Prerequisite: Mathematics 208. (MA308) |

Numerical Analysis | Iterative methods for approximating numerical solutions to systems of equations, polynomials, integral and differential equations. Also matrix manipulation and error analysis. Prerequisite: Mathematics 240 or consent of instructor. (MA313) |

Advanced Mathematical Statistics | Continuation of Mathematics 304 with an emphasis on multivariate distributions, estimation and tests of statistical hypotheses. Students who complete the course will have the opportunity to be prepared for the first actuarial statistics examination. Prerequisite: Mathematics 304. (MA314) |

History of Mathematics | A study of major developments in the history of mathematics and in the mathematical contributions of non-Western cultures. The interplay between mathematics and culture is emphasized. Prerequisite: MA140 or consent of instructor. (MA320) |

Theory of Interest | This course is designed to prepare students for Exam FM that is administered by the Society of Actuaries. Topics include compound interest formulas, annuities, perpetuities, amortization schedules, bonds, and other securities. Prerequisite: a grade of C- or better in MA240. (MA324) |

Mathematical Physics | We will discuss applications of mathematics to various areas of physics. Topics may include vector calculus, linear algebra, differential equations, series solutions to differential equations, Fourier series, special functions, and calculus of variations. The primary audience for this course is sophomore and juniors majors who are preparing to take Analytical Mechanics, Electrodynamics, or Quantum Mechanics, although applied mathematics majors may find the course useful. Cross-listed with PY325. Prerequisities: PY152 and MA240, or consent of instructor. Recommended Co-Requisites: MA250 and/or MA303. (MA325) |

Algorithms and Data Structures | Study of algorithms and data structures. Prerequisite: MA208 or consent of instructor. (MA337) |

Calculus III | Introduction to calculus of several variables, partial derivatives, multiple and iterated integrals, vector functions. Prerequisite: Mathematics 240. (MA340) |

Artificial Intelligence | Introduction to the theory and practice of artificial intelligence. Topic areas selected from heuristic search techniques, knowledge representation, symbolic reasoning, fuzzy logic, planning, learning, natural language processing, expert systems, genetic programming, intelligent agents, swarm intelligence, and neural networks. Rerequisite: MA208 and MA337. (MA342) |

Abstract Algebra | Introduction to abstract algebra. Includes basic ideas and theorems about groups, rings, integral domains, and fields. Prerequisite: Mathematics 303 or consent of instructor. (MA408) |

Mathematical Logic | An introduction to mathematical logic and metamathematics. Includes predicate calculus, proof theory, formal axiomatic theories, consistency, completeness, and decidability. Prerequisite: MA 208 or consent of instructor. (MA420) |

Methods of Teaching Mathematics in Grades 6-12 | Microteaching and structured classroom participation required. The course focuses on teaching standards based mathematics content with the inclusion of appropriate technologies. Required for both middle school and high school Illinois Mathematics Teacher Certification. Prerequisites: a grade of C or better in MA140 plus grades of C or better in an additional 9 hours of mathematics above MA140, junior or senior standing, admission to the School of Education, and consent of instructor. (MA425) |

Advanced Calculus | A rigorous treatment of fundamental analysis concepts. Includes topology of the real number system, limits, continuity, sequences, differentiability, and integrability. Prerequisite: MA 303 and MA 340, or consent of instructor. (MA440) |

Internship in Methods of Teaching Mathematics | Students learn methods of teaching mathematics in a classroom situation under the supervision of a member of the department. Includes methods of course organization, presentation, and assessment and the use of technology in teaching mathematics. Prerequisite: Junior mathematics major and approval of instructor and Department chair. (MA471) |

Internship | An on-the-job professional experience working for an organization, business or University department during an academic semester. A supervised work experience in which the superior student's mathematical background is used in an actual working environment. Prerequisite: Junior mathematics major and approval of instructor and Department chair. (MA472) |

Independent Study | Advanced study in a topic chosen jointly by student and instructor. Some recent topics include topology, real analysis, operations research, complex analysis, logic and foundations, ethnomathematics, advanced statistics, formal language theory, projective geometry and computer-assisted instruction in mathematics. Prerequisite: Consent of department chair. (MA491, MA492, MA493, MA494) |

Senior Seminar | Research in applied mathematics. Students create and present a research project under the direction of a member of the mathematics faculty. Prerequisite: Senior mathematics major. (MA499) |