Mathematics

Changes effective Fall Term 2014

Anderson, M. |
Boyd |
Myers |
Rejniak |

Seitzer |
Teymuroglu |
Vitray |
Yellen |

One of the distinguishing characteristics of the Department of Mathematics and Computer Science is its commitment to quality teaching, which promotes active learning on the part of students. Faculty work closely with students to ensure that each has a successful educational experience. To this end, the department has been involved in the calculus reform movement since its beginnings and, as a result, nonlecture methods, coupled with technology, are used in many classes.

The Rollins mathematics curriculum is flexible enough to prepare a major for a wide choice of career options, such as graduate work in pure or applied mathematics, statistics, economics, secondary education, actuarial science, government, industry, or law school.

**MAJOR REQUIREMENTS**

Fourteen (14) courses are required: ten (10) core courses and four (4) electives.

CORE COURSES

**MAT 111 Calculus I****MAT 112 Calculus II****MAT 140 Introduction to Discrete Mathematics****MAT 211 Calculus III****MAT 219 Probability and Statistics****MAT 230 Linear Algebra****MAT 330 Proof and Abstraction****MAT 455 Real Analysis****OR****MAT 475 Abstract Algebra I****MAT 485 Senior Seminar in Mathematics****CMS 167A/167B Introduction to Computing**

ELECTIVES

Four (4) additional courses in mathematics: two (2) at or above the ** 300 level** and two (2) at the

TYPICAL SCHEDULE

There are a variety of ways in which students interested in mathematics can complete the major. However, by the end of the junior year, majors should complete all core courses numbered ** 330** or below and have taken one elective. This will leave

**MINOR REQUIREMENTS**

Eight (8) courses from the major requirements, excluding ** MAT 485**.

** MAT 103 Quantitative Reasoning:** Covers collection of data and analysis of everyday quantitative information using spreadsheets or statistical packages. Touches upon population vs. sample, parameter vs. statistic, variable type, graphs, measures of center and variation, regression analysis, and hypothesis testing.

**MAT 106 Geometry for Teachers:** Explores fundamental concepts of Euclidean geometry, transformational geometry, and graph theory, including area, volume, and scaling; polygons, polyhedra, and angles; and circles, spheres, and symmetry.

**MAT 107 Mathematics for Teachers****:** Explores areas of mathematics of importance to elementary school teachers. Emphasis on developing students' ability to solve problems in the areas of set theory, number theory, algebra, and geometry.

**MAT 108 Essential Math:** Basic mathematical competency course required for Rollins Plan students. Covers displaying and describing data; functions including linear, exponential and multivariable; linear regression and correlation; and basic probability. *Prerequisite*: high school Algebra II. *Co-requisite: MAT 108L*

**MAT 108L Essential Math Lab**: Develops proficiency in the use of spreadsheets to prepare students for MAT 108. Topics include formulas, charts and graphs, autofill, tables and pivot tables, and sorting. *Co-requisite: MAT 108*.

**MAT 109 Precalculus Mathematics:** Discusses function, including behavior and properties of elementary functions -- polynomial, rational, exponential, and trigonometric. Stresses understanding of graphs through use of graphing calculator. Requires review of algebra but no use of calculus. Prepares students for** MAT 110** and

**MAT 110 Applied Calculus:** Applies concept of derivative to economics, business, and life sciences. Includes partial differentiation with applications. *Prerequisite*: * MAT 109* or consent. Not open to students with credit in

**MAT 111 Calculus I:** Investigates functions using fundamentals of calculus: limit, derivative, and integral. Uses current technology to support graphical, numeric, and symbolic approaches. *Prerequisite*: high school precalculus or equivalent.

**MAT 112 Calculus II:** Emphasizes applications of integrals, methods of integration, power series, and differential equations in the continuing investigation of functions. *Prerequisite: MAT 111.*

**MAT 140 Introduction to Discrete Mathematics:** Provides the foundation essential for sound mathematical reasoning and computer science. Topics include, but are not restricted to, propositional and predicate logic; proof strategies and induction; sets, functions, and recursion; elementary counting techniques; and number systems.

**MAT 201 Mathematics of Gaming:** Uncovers the mathematics behind games of chance. Students will learn probability theory and statistical methods through the study of such games as roulette, craps, backgammon, poker, and blackjack. Suitable for nonmajors. *Prerequisite:* sophomore, junior, or senior standing.

**MAT 211 Calculus III:** Follows ** MAT 112****. ** Explores vectors, directional derivatives, and gradient; functions of several variables; partial derivatives and applications; multiple integrals; and other coordinate systems. *Prerequisite: MAT 112*.

**MAT 219 Probability and Statistics:** Delves into sample spaces, conditional probability, random variables, expectations and distributions, moment-generating functions, central-limit theorem, and introduction to estimation, confidence intervals, and hypothesis testing. *Prerequisites: MAT 112* or *MAT 140*.

**MAT 230 Linear Algebra:** Highlights connections between matrices and systems of equations. Uses technology extensively to examine Euclidean n-space, linear independence, spanning, bases, Gaussian elimination, matrix algebra, determinants, eigen values and eigenvectors, and Gram-Schmidt orthogonalization. *Prerequisite: MAT 111* or*CMS 167A/167B.*

**MAT 301 Non-Euclidean Geometry**: Delves into the realms of Euclidean and Non-Euclidean geometries. Studies finite geometries, neutral geometry, Euclidean geometry, and hyperbolic geometry. *Prerequisite:* one *200-level* *MAT* course.

**MAT 305 Ordinary Differential Equations: **Examines first-order equations and theory of linear differential equations: series solutions, systems of linear differential equations, and basic boundary-value problems and eigen values.

**MAT 310 Applied Discrete Mathematics**: Builds on the foundation established in *Introduction to Discrete Mathematics*. Topics include, but are not restricted to, combinatorics and graph theory, Boolean algebra, digital logic circuits, functional programming, models of computation, and computational complexity. *Prerequisite: MAT 140.*

**MAT 320 Math Methods for Physical Sciences I:** Covers series expansions, complex numbers, linear algebra, and multi-variable calculus. *Prerequisite: MAT 112* or equivalent preparation.

**MAT 330 Proof and Abstraction:** Studies logic (including quantifiers) as well as sets, relations (including equivalence and order relations), functions (1-1, onto), and induction. Students test conjectures, write proofs, and provide counterexamples. Prerequisite: MAT 140 orMAT 230.

**MAT 340 Models and Algorithms in Graph Theory:** An applications-oriented course in graph theory. Topics include properties and representations of graphs, models, trees, connectivity, and traversal and graph-coloring algorithms. Applications are likely to include Chinese-Postman, Traveling-Salesman, software-testing, and time tabling. *Prerequisite:* *MAT 140.*

**MAT 350 Actuarial Mathematics**. Introductory course in actuarial mathematics. An actuary is a professional who measures and analyzes the financial cost of risk. Describes and discusses the concepts and techniques used in interest rate theory and financial modeling. Students will gain expertise in interest rates and factors, level annuities and varying annuities, financial instruments, and stochastic interest rates. Prerequisite: * MAT 112*.

**MAT 370 Mathematical Statistics I:** Introduces random variables, moment-generating functions, functions of random variables, limit laws, point estimations and statistical inference, tests of hypotheses, and interval estimation. Uses commercial statistical packages. *Prerequisites: MAT 211* and*MAT 219.*

**MAT 390/490 Topics in Mathematics:** An intensive introduction to a specialized area of mathematics. *Prerequisite:* for *MAT 390*, *MAT 140* or *230*; for *MAT 490, MAT 330.*

**MAT 398 Directed Study:** Supervises individual study on such advanced topics as differential equations, linear programming, game theory, probability and statistics, and model theory. May be repeated for credit.

**MAT 410 Pure and Applied Graph Theory:** Topics include connectivity, traversals, network flow, and colorings, with balance given to theoretical aspects and their application to various areas in computer science, operations research, science, and engineering. *Prerequisites: MAT 140* and any *300-level* *MAT* course.

**MAT 419 Probabilistic Methods in Operations Research:** Applications-oriented operations research course that introduces a variety of probability models and solution methods to solve a broad range of real-world problems in science, financial engineering, economics, and management science. *Prerequisites: ***MAT 219** and one *300-* or *400-level* *MAT* course.

**MAT 440 Coding Theory:** Investigates means of encoding information in such a way as to be able to detect and/or correct transmission errors efficiently. *Prerequisite: ***MAT 330***.*

**MAT 450 Mathematical Modeling:** Emphasizes creation of mathematical models representing real-world situations and use of models to formulate reasonable solutions to problems. Explores concepts from graph theory, probability, linear algebra, and differential equations. *Prerequisites: ***MAT 140, MAT 219, MAT 230, and MAT 305***.*

**MAT 455 Real Analysis:** Examines structure of real numbers, including completeness, topological properties, limits of sequences, continuity, uniform continuity, boundedness, and derivatives. Students write proofs and produce counterexamples. *Prerequisites: ***MAT 112** and** MAT 330***.*

**MAT 460 Complex Analysis: **A rigorous study of the functions of a complex variable. Topics include complex derivatives, contour integrals, series representations of analytic functions, residues, and some applications. Prerequisites: **MAT 112** and **MAT 330.**

**MAT 470 Mathematical Statistics II:** Continues Mathematical Statistics I with ranking and selection procedures, decision theory, nonparametric statistical inference, regression and linear statistical inference, multivariate analysis, and time-series analysis. Uses commercial statistical packages. *Prerequisites: ***MAT 230** and **MAT 370***.*

**MAT 475 Abstract Algebra I:** Acquaints students with large collection of groups and with Cayley's theorem, Lagrange's theorem, and fundamental homomorphism theorem. Emphasizes production of accurate, concise proofs. *Prerequisite: ***MAT 330***.*

**MAT 485 Senior Seminar in Mathematics:** Requires students to prepare, deliver, and evaluate oral presentations based on their readings of mathematical literature. *Prerequisite:* one *400-level MAT* course or consent.

**MAT 499 Independent Study:** Covers selected topics in mathematics. May be repeated for credit.