# Department of Mathematics

Dr. John E. Hammett III, *Chairperson*

The Department of Mathematics offers a major and a minor in Mathematics. Students must maintain an average of at least 2.0 in all mathematics courses counted towards the major in order to graduate as mathematics majors.

## Requirements for Mathematics Major

### Degree of Bachelor of Science

Eight of the required credits for the major count towards the Core Curriculum Requirements.

MA-143 | Differential Calculus ^{1} | 4 |

MA-144 | Integral Calculus ^{1} | 4 |

MA-246 | Discrete Mathematics | 3 |

MA-247 | Introductory Linear Algebra | 3 |

MA-248 | Math Tech Lab | 1 |

MA-273 | Multivariable Calculus I ^{1} | 4 |

MA-274 | Multivariable Calculus II ^{1} | 4 |

MA-335 | Probability Theory | 3 |

MA-375 | Advanced Calculus | 3 |

or MA-377 | Ordinary Differential Equations | |

MA-382 | Mathematical Modeling | 3 |

or MA-385 | Topics in Applied Mathematics | |

MA-441 | Modern Algebra | 3 |

MA-490 | Senior Seminar in Mathematics (Capstone) | 3 |

MA | Three Mathematics Electives (MA-335 or higher) | 9 |

Total Credits | 47 |

^{1} | May count towards the Core Mathematics Requirement. |

#### Special Notes on Core Curriculum Requirements

^{1} | The Core Curriculum Natural Science Requirement for Mathematics majors is ordinarily PC-185 General Physics I, and CS-180 Introduction to Programming. Mathematics majors are encouraged to take PC-186 as well. A more advanced course in computer programming may substitute for CS-180, but a course in computer programming is expected. |

^{2} | Mathematics majors are encouraged to take EC-101 Macroeconomic Principles as part of their Social Sciences Requirement. |

^{3} | Courses numbered below the 100-level do not fulfill the Mathematics Core Requirement for the Bachelor’s degree. |

^{4} | Ordinarily a student may not receive credit for more than one of the calculus sequences, nor may a student receive credit for both MA-103 Mathematics for the Humanities II and MA-106 Introduction to Probability and Statistics, nor may a student receive credit for both MA-132 Statistics for the Life Sciences and MA-212 Elementary Statistics. |

^{5} | Completion of the Mathematics Core Requirement is ordinarily a prerequisite for any mathematics courses numbered 200 or above. |

^{6} | Satisfactory completion of developmental mathematics (MA-001 for Elementary Applied Mathematics, Intro to Probability and Statistics, Mathematics for the Humanities and Mathematics for Educators; MA-101 Precalculus for Calculus), or exemption by placement testing results, is prerequisite for core mathematics courses. |

^{7} | Students who receive advanced placement beyond the introductory calculus sequences may use MA-273 Multivariable Calculus I and MA-274 Multivariable Calculus II to satisfy the Mathematics Core Requirement. |

#### Special Notes on Major Requirements

^{1} | In order to continue as mathematics majors, students must maintain an average of at least 2.0 in MA-143, MA-144, MA-246, MA-247, MA-248, MA-273, and MA-274. |

^{2} | The Chairperson of the Mathematics Department may reduce the 9 credit requirement in the Mathematics electives to 3 credits if the student has, in consultation with a departmental advisor, combined a Mathematics major with a specified program of courses in a related field. Such programs include, but are not limited to, major or minor programs in another department and the certification program in secondary education. |

## Requirements for a Minor in Mathematics

Select one of the following calculus sequences: | 6-8 | |

Elementary Calculus I and Elementary Calculus II | ||

Statistics for the Life Sciences and Calculus for the Life Sciences | ||

Differential Calculus and Integral Calculus | ||

Multivariable Calculus I and Multivariable Calculus II | ||

Select 4 MA-courses, 200-level or above | 12 | |

Total Credits | 18-20 |

#### Special Notes on Minor Requirements

^{1} | Students wishing to minor in mathematics should meet with the department Chairperson to choose appropriate electives to match or complement their major. |

^{2} | A student must maintain an average of at least 2.0 in the courses presented for the mathematics minor. |

### Courses

**MA-001. Introductory Algebra. 3 Credits.**

Real numbers, variable expressions, solving equations, linear equations in two variables, systems of linear equations, inequalities. This is a preparation course for MA-102, MA-105, MA-106, and MA-101.

**MA-101. Precalculus. 3 Credits.**

Brief review of basic algebraic concepts; functions (general concepts, linear, quadratic); polynomial and rational functions; exponential and logarithmic functions; summary of trigonometric functions; application problems.

**MA-102. Mathematics for the Humanities I. 3 Credits.**

Symbolic logic, number theory, functions, and other topics selected by the instructor.

**MA-103. Mathematics for the Humanities II. 3 Credits.**

Set theory, combinatorics, finite probability, conditional probability, and topology. Prerequisites: MA-102.

**MA-105. Elementary Applied Mathematics. 3 Credits.**

Introduction to ways in which everyday situations can be modeled and studied mathematically: networks, voting, coding, and finance.

**MA-106. Introduction to Probability and Statistics. 3 Credits.**

Describing data collections using measures (e.g., center and spread) and graphical representations (e.g., histograms and plots), estimating probabilities for discrete and continuous distributions, and making statistical inferences using selected approaches (e.g., confidence intervals, hypothesis testing, linear regression analysis).

**MA-108. Mathematics for Educators I. 3 Credits.**

In-depth study of the concepts that underlie the mathematics of the elementary school curriculum in the United States. Topics include set theory, numeration, mathematical thinking, number theory, and the four basic operations of mathematics. This course is intended for individuals who expect to teach in primary school.

**MA-109. Mathematics for Educators II. 3 Credits.**

This course is a continuation of MA-108. Topics in the second semester include the real number system, proportional reasoning, statistics, probability, and measurement systems. This course is intended for individuals who expect to teach in primary school. Prerequisites: MA-108.

**MA-115. Mathematics for the Health Sciences. 3 Credits.**

This course is designed for students in nursing, pre-health and allied-health fields so that they can master skills of basic math, use of measurement systems, and strategies of problem solving needed in the health-science courses. The Metric System of Measurement; Apothecaries' and Household Systems of Measurement; Calculations needed to determine dosages; Construction and Reading of Graphs; Introduction to Statistics including measures of central tendency and measures of dispersion.

**MA-123. Elementary Calculus I. 3 Credits.**

Differential calculus of polynomial and rational functions; applications of calculus to problems in business, economics, and the life sciences.

**MA-124. Elementary Calculus II. 3 Credits.**

Exponential and logarithmic functions, integral calculus, differential equations applications to problems in business, economics, and the life sciences. Prerequisites: MA-123.

**MA-125. Intermediate Calculus. 2 Credits.**

This course is intended for students (e.g., computer science majors) who have completed 6 credits of calculus and who now wish to take Multivariable Calculus. Prerequisites: MA-124.

**MA-132. Statistics for the Life Sciences. 3 Credits.**

Basic methods of data analysis. Topics include displaying data graphically; measures of central tendency and variability; probability concepts; normal, t, chi-square, and F distributions; confidence intervals and estimation; hypothesis testing; regression and correlation analysis; analysis of variance; contingency tables; use of statistical software. Biological applications are emphasized.

**MA-133. Calculus for the Life Sciences. 4 Credits.**

Polynomial, rational, and trigonometric functions; limits, continuity, derivatives; graphs, maximum-minimum problems; exponential and logarithmic functions, growth and decay problems integrals, basic integration techniques, applications of the integral. Biological applications are emphasized.

**MA-143. Differential Calculus. 4 Credits.**

Limits and continuity; the derivative; chain rule and differentiation of algebraic functions; extrema; applications; the Mean Value Theorem.

**MA-144. Integral Calculus. 4 Credits.**

The definite integral and the Fundamental Theorem of the Calculus applications transcendental functions methods of integration. Prerequisites: MA-143.

**MA-212. Elementary Statistics. 3 Credits.**

Descriptive statistics, laws of probability, some standard probability functions, central limit theorem, confidence intervals, hypothesis testing. Prerequisites: MA-106(13047), MA-115, MA-124, OR INSTRUCTOR PERMISSION.

**MA-214. Mathematics of Finance. 3 Credits.**

Interest, partial payment, ordinary annuities, depreciation, amortization, sinking funds bonds, deferred annuities, perpetuities probability, mortality tables, life annuities, life insurance. Prerequisites: EITHER MA-106 MA-124 MA-133 MA-144 OR MA-273.

**MA-216. Computer Mathematics. 3 Credits.**

Number systems, internal representation, errors logic, Boolean algebra, circuits algorithms, efficiency counting, probability. Prerequisites: EITHER MA-106 MA-124 MA-133 MA-144 OR MA-273, AND CS-180.

**MA-218. Quantitative Methods for Business. 3 Credits.**

Decision theory, trees linear programming, simplex method, sensitivity analysis inventory theory CPM, PERT. Prerequisites: MA-106, MA-124, OR INSTRUCTOR PERMISSION.

**MA-222. Intermediate Statistics. 3 Credits.**

This course extends the statistical data analysis introduced in MA-212. Students will explore additional topics in parametric and non-parametric methods, including analysis of variance (ANOVA) and multiple regression learners will also actively design statistical experiments and interpret data sets. Students will use statistical software and computer programming as tools to assist with data analysis. Prerequisites: MA-212.

**MA-246. Discrete Mathematics. 3 Credits.**

A study of the variety of finite mathematical structures and their applications. Logic and proofs Boolean algebras and combinatorial circuits sets, relations, equivalence relations, and recurrence relations graphs, trees. Prerequisites: MA-144 OR MA-125.

**MA-247. Introductory Linear Algebra. 3 Credits.**

Matrix calculus vector spaces linear independence and bases linear transformations on vector spaces eigenvalues and eigenvectors. Prerequisites: MA-246.

**MA-248. Math Tech Lab. 1 Credit.**

Software for numerical and symbolic computations (such as MatLab and Mathematica), and mathematical typesetting (such as TeX) Prerequisites: MA-144 OR MA-125 OR INSTRUCTOR PERMISSION.

**MA-273. Multivariable Calculus I. 4 Credits.**

Integration techniques, 2-and-3 dimensional vector geometry functions of several variables, limits, directional derivatives, partial differentiation, extrema double and Triple integrals. Prerequisites: MA-144 OR MA-125.

**MA-274. Multivariable Calculus II. 4 Credits.**

Limits and L'Hospital's Rule improper integrals infinite sequences and series power series, Taylor series selected topics in multivariable calculus. Prerequisites: MA-273.

**MA-295. Co-Op. 3 Credits.**

Co-operative work experience.

**MA-302. Elementary Math Functions for Middle School. 3 Credits.**

Functions and equations, arithmetic and geometric sequences, mathematical methods, linear functions, difference equations, quadratic and cubic functions, exponential and logarithmic functions, domain and range, fitting a line to data and modeling, and associated mathematical processes. Methods for learning and teaching the topics are addressed concurrently with the content.

**MA-304. Statistics, Probability and Discrete Math for Middle School. 3 Credits.**

Topics include collecting, summarizing, and interpreting data, sampling techniques, fundamental concepts of probability, counting techniques, Euler and Hamiltonian circuits, shortest distance algorithms, and associated mathematical processes. Methods for learning and teaching the topics are addressed concurrently with the content.

**MA-306. Geometry for Middle School. 3 Credits.**

Metric and US standard measurement, inductive and deductive reasoning, Euclidean geometry of two and three-dimensional figures including, but not limited to: area, perimeter, volume, surface area, congruency, similarity, rotation and transformation. Coordinate geometry, iteration and fractals, geometry in the world around us, and associated mathematical processes. Methods for learning and teaching the topics are addressed concurrently with the content.

**MA-335. Probability Theory. 3 Credits.**

Probability spaces, random variables, expectation, variance, standard deviation, binomial, multinomial, and Poisson distributions approximations by the normal distribution Chebyshev's Inequality. Prerequisites: MA-273.

**MA-336. Mathematical Statistics. 3 Credits.**

Law of large numbers, Central Limit Theorem, estimation of parameters, confidence intervals, test of hypotheses, sampling, regression, analysis of variance. Prerequisites: MA-335.

**MA-350. College Geometry. 3 Credits.**

Study of Euclidean and other geometries from an axiomatic point of view. Prerequisites: MA-246.

**MA-375. Advanced Calculus. 3 Credits.**

Real numbers, sequences, limits of sequences and functions, continuity, differentiation, theory of integration, pointwise and uniform convergence. Prerequisites: MA-274.

**MA-377. Ordinary Differential Equations. 3 Credits.**

Existence and uniqueness of solutions first and second order equations systems of linear differential equations solutions in power series applications. Prerequisites: MA-247 AND MA-274.

**MA-379. Differential Equations for Engineers. 4 Credits.**

This Course is an Expanded Version of MA-377 and includes the following additional topics: The Laplace Transform, Partial Differential Equations and Fourier Series. Prerequisites: MA-274 AND MA-247.

**MA-382. Mathematical Modeling. 3 Credits.**

The nature and philosophy of model building algebraic and analytic models in the social, physical, and life sciences. Prerequisites: MA-273 AND MA-247.

**MA-385. Topics in Applied Mathematics. 3 Credits.**

**MA-399. Tutorial. 3 Credits.**

**MA-441. Modern Algebra. 3 Credits.**

Introduction to modern algebraic concepts theory of groups, rings, and fields. Prerequisites: MA-246 MA-247 INSTRUCTOR CONSENT REQUIRED.

**MA-467. Functions of a Complex Variable. 3 Credits.**

Complex numbers, analytic functions, elementary functions, mapping of elementary functions, integrals. Prerequisites: MA-274.

**MA-490. Senior Seminar in Mathematics. 3 Credits.**

In this capstone course, graduating senior Mathematics majors will explore areas of mathematics that draw on many of the previous courses, emphasizing the connection between different areas of mathematics. This culminating academic experience for the major will include writing, presentations, and contemporary mathematics research. Prerequisites: MA-441 SENIOR MATHEMATICS MAJORS ONLY.

**MA-495. Undergraduate Research. 3 Credits.**

Original research topic, chosen in consultation with faculty and pursued under faculty supervision.