Mathematics

Faculty

Research

The Department of Mathematics offers Directed Reading courses every term for highly motivated students to pursue individual directed research. DR's in recent years have included: Problem Solving, Complex Analysis, Introductory Topology, Knot Theory, Advanced Calculus, and Boolean Algebra. Any student can request a Directed Reading in an area of their interest - if that interest matches interests of one of the faculty.

The department also has an active Math Circle and Problem Solving Class. Students attend guest lectures at the University of South Alabama and learn problem-solving skills two nights a week at ASMS. Students participate in Regional, Statewide, and National competitions, including Mandelbrot, American Mathematical Competition, and the University of Alabama High School Math Competition.

Graduation Requirements

4.0 CU graduation requirement. Continuous enrollment until graduation requirement is met. Credits must include Trigonometry & Precalculus and one 0.5 CU math course beyond Precalculus. For all entering students a math placement exam will be used to evaluate the appropriate starting level in the mathematics sequence. If Geometry has not been completed prior to entering ASMS, it should be completed during the first year at ASMS.

Concentration/Distinction Requirements

For a Concentration, a student must complete three (3) courses (1.5 CU) beyond Differential Calculus, at least one of which must be from the Calculus sequence. For a Distinction, a student must complete six (6) courses (3 CU) beyond Differential Calculus, at least two of which must be from the Calculus sequence. The Calculus sequence includes Integral Calculus, BC Calculus, and Multivariable Calculus. For both Concentration and Distinction, the following requirements and restrictions apply: all grades in all math courses must be B or higher, and overall math GPA must be 3.6 or higher; no course except for a Directed Reading may count more than once (0.5 CU max), and a Directed Reading may count no more than three times (0.75 CU max); Computer Science courses do not count toward a concentration or distinction in Mathematics.

Course Descriptions

MA061     Geometry 1/2     .5 CU
Geometry I is an introduction to Euclidean Geometry, including the nature of reasoning and proof involved in the study of geometry. Topics covered include congruent and similar figures, parallel lines, and planes, plus an introduction to the study of area, volumes and transformations involving both investigations and deductive proof. Prerequisite: none.

MA062     Geometry 2/2     .5 CU
Geometry II involves Euclidean Geometry of the circle and associated concurrence theorems, the study of analytic geometry of the various conic sections, and an investigative approach to the study of elementary topology, fractal geometry and non-Euclidean geometry. Prerequisite: MA061.

MA100     Intermediate Algebra     .5 CU
This course introduces algebra topics such as polynomials, factoring, exponents and radicals, linear and quadratic equations, functions, graphs, systems of equations, and applications. The course prepares students for Accelerated Algebra. Prerequisite: none.

MA101     Accelerated Algebra     .5 CU
Accelerated Algebra covers, in greater depth, many of the topics that are introduced in Intermediate Algebra. Additional topics covered include complex numbers, quadratic and rational inequalities, and inverse functions. The course is equivalent to a typical college algebra course. Prerequisite: MA100 or equivalent score on math placement test.

MA103     Trigonometry     .5 CU
Trigonometry studies trigonometric functions, inverse trigonometric functions, graphs, identities, vectors, complex number representations, solving triangles and trigonometric equations, and applications. Prerequisite: MA101 or equivalent score on math placement test. The course must be completed by the end of the junior year.

MA104     Precalculus     .5 CU
Precalculus is a survey of topics necessary for calculus, including polynomials, rational, exponential and logarithmic functions, matrices, sequences and series, and the binomial theorem. Prerequisite: MA101 or equivalent score on math placement test.

MA200     Problem Solving     .25 CU
The Problem Solving Seminar/Mathematics Circle is designed to teach mathematics as a thinking tool more than as a computational tool. As such it will benefit students, whose studies lead them into any problem solving discipline, including fields as far removed from mathematics as economics, chemistry, engineering, or even business. The mission of the Problem Solving/ Mathematics Circle/Math Team Preparation is to introduce students to mathematics as a creative thinking tool through problem solving. Prerequisites: none.

MA201     Differential Calculus     .5 CU
This introduction to the theory, techniques, and applications of differential calculus includes functions, limits, derivatives, related rates, maximum/minimum problems, and curve sketching, derivatives related to exponential, logarithmic, trigonometric and inverse trigonometric functions. Prerequisites: ‘B’ or better in both MA103 and MA104 or permission of the department.

MA202     Integral Calculus     .5 CU
This introduction to the theory, techniques, and applications of integral calculus includes indefinite and definite integrals, area, volume, work, fluid force, integrals related to exponential, logarithmic, trigonometric and inverse trigonometric functions, and integration techniques. Prerequisite: ‘B’ or better in MA201 or permission of the department. NOTE: Students who plan to take the AP Calculus AB exam should complete MA201 and MA202.

MA203     BC Calculus     .5 CU
BC Calculus studies a variety of calculus topics including infinite sequences and series, and parametric and polar equations. Other topics might include conic sections, introduction to differential equations and hyperbolic functions. Prerequisite: ‘B’ or better in MA202 or permission of the department. NOTE: Students who plan to take the AP Calculus BC exam should complete the calculus sequence through MA203.

MA205     Introduction to Statistics     .5 CU
This course focuses on the statistical methods and reasoning, which are used in the natural and social sciences. Topics include: organizing, classifying, and comparing data; probability distributions, sampling distributions, estimation and hypothesis testing. Prerequisite: MA104.

MA206     Discrete Mathematics     .5 CU
This course studies the mathematical elements of computer science including propositional logic, predicate logic, sets, functions and relations, combinatorics, mathematical induction, recursion, algorithms, matrices, graphs, trees, and Boolean logic. Prerequisite: MA104.

MA207     Visual Mathematics     .5 CU
This is a hands-on course designed to allow students to visually explore mathematical topics such as symmetry, modeling, and fractals. Prerequisite: MA104.

MA301     Multivariable Calculus     .5 CU
Multivariable Calculus studies the calculus of functions of two or more free variables including partial derivatives, gradients and directional derivatives, max-min problems, LaGrange Multipliers, multiple integrals, cylindrical and spherical coordinates, line integrals, Green’s and Stokes’ Theorems, and the Divergence Theorem. Prerequisite: ‘B’ or better in MA202 or permission of the department.

MA401     Differential Equations     .5 CU
Differential Equations introduces the theory, techniques, and applications of ordinary differential equations. Topics include first and second order differential equations, linear equations of higher order, systems of differential equations, numerical methods, Laplace transform methods, and applications. Prerequisite: ‘B’ or better in MA202 or permission of the department.

MA402     Linear Algebra     .5 CU
Linear Algebra studies the theory, techniques, and applications of linear algebra including systems of linear equations, matrices, determinants, vectors, vector spaces, and eigenvalues/eigenvectors. Prerequisite: ‘B’ or better in MA201 or permission of the department.

MA403     Complex Analysis     .5 CU
This course is an introduction to the analysis of complex functions. Topics covered: arithmetic of complex numbers; regions in the complex plane; limits, continuity, and derivatives of complex functions; elementary complex functions; mappings by elementary functions; contour integration; power series; Taylor series; Laurent series; calculus or residues; conformal representation; applications. Prerequisite: 'B' or better in MA202 or permission of the department.

MA404     Number Theory     .5 CU
This course is an introduction to classical number theory with a balance of theory and computation. Topics include mathematics induction, divisibility properties, and properties of prime numbers, the theory to congruencies, number theoretic functions, and continued fractions. Prerequisite: MA201.

MA405     Numerical Mathematics     .5 CU
This course is an investigation of methods of numerical computation with an emphasis on application of numerical approximation techniques in the solution of problems frequently encountered in engineering and science. Topics will include error analysis, solutions of equations, interpolation, quadrature, and linear systems. Prerequisite: MA202.

MA410     AP Calculus Review     .5 CU
This course will focus on preparation for the AP Calculus exam. Prerequisite: students who plan to take the AP Calculus AB exam should complete MA201 and MA202; students who plan to take the AP Calculus BC exam should complete the calculus sequence through MA203.