Mathematics Courses

Prerequisites

Almost all of our mathematics and computer science courses have prerequisites. Introductory courses require mastery of elementary skills as demonstrated by the combination of a student's high school preparation and a satisfactory placement test score. Enrollment in courses beyond the introductory level require successful completion of another Albion course as listed in the catalog or comparable course at another institution. Students taking an advanced course should have at least a 2.0 in all prerequisite courses. The purpose of a prerequisite is to ensure a student has a solid foundation of necessary skills required to succeed in completing course objectives. Prerequisites protect students by ensuring they are not asked to perform activities for which they are not prepared. We have established the prerequisites for our courses to help students have a coherent learning experience.

Prerequisites are strictly enforced. Before enrolling in a course, all of its prerequisites must be completed. A student enrolled in a course will be dropped from the course if they have do not have the prerequisites. In a few special situations a student may be granted permission to enroll in a course without a prerequisite. These situations are rare and must be approved in consultation with the student's academic advisor and the course instructor. The instructor of the course and department chair have the final decision to waive a prerequisite. Students granted a waiver cannot expect the course to be taught at a lower level or demand the instructor teach prerequisite material. Expectations of all students in a course are the same even if a waiver of a prerequisite is granted.

104 Mathematics for Elementary Teachers 1 unit
Spring
Prerequisites: Three years of college-preparatory mathematics (or its equivalent). Priority given to students in the elementary education program.
An investigation of mathematics (arithmetic, geometry, algebra, problem solving) for elementary school teachers. Topics will be chosen from: sets, relations and functions; numeration systems; whole numbers and their operations; number theory; rational numbers and fractions; decimals and real numbers; geometry and measurement; and probability and statistics. The emphases will be on doing mathematics, using manipulatives and developing intuition and problem-solving skills. Laboratory.

109 Statistical Methods 1 unit
Fall, Spring
Prerequisite: Permission of instructor.
Descriptive statistics, probability, sampling distributions, hypothesis testing, parameter estimation, confidence intervals, linear regression, curve fitting, analysis of variance and non-parametric statistics are discussed. The Minitab statistics package is used. Students may not receive credit for both Mathematics 109 and 210. Usually not open to students who have had Mathematics 141.

119 Finite Mathematics for Decision Making 1 unit
Spring
An introduction to discrete mathematics. Applications are drawn from diverse areas including biological sciences, economics, political science and personal finance. Topics in discrete mathematics typically include graph theory, management science, statistics, the mathematics of social choice, game theory, and the logical foundations of mathematics. Interconnections among science, mathematics, and technology with society, environment, and self are central themes. The course is designed for non-majors.

125 Functions 1 unit
Fall, Spring
A modern, unified approach to algebra, trigonometry, logarithms and analytical geometry based on the concept of a function. Linear equations and inequalities, quadratic equations and inequalities, polynomials and rational functions, logarithms and exponential functions, trigonometric and inverse trigonometric functions, and analytic geometry (the circle, the parabola, the ellipse and the hyperbola) will be covered. Emphasis will be given to the use of graphing calculators and on the use of mathematics as a problem-solving tool. Applications in natural science, social science and business will be discussed. This course also serves as a preparation for calculus. Well-prepared students who already have a strong working knowledge of algebra, trigonometry, and logarithms should elect Mathematics 141 in place of Mathematics 125. A graphing calculator is required.

141 Calculus of a Single Variable I 1 unit
Fall, Spring
Prerequisite: Mathematics 125 or equivalent.
Mathematics 141 and 143 constitute a thorough introduction to calculus for students who intend to continue in mathematics and for those who will use calculus in other fields such as science and engineering. Mathematics 141 covers limits, continuity, derivatives and a brief introduction to integration. Applications to problems in related rates, optimization, solid geometry and elementary mechanics are covered. Requires a strong working knowledge of algebra and trigonometry. Students who are weak in these areas should elect Mathematics 125. A graphing calculator is required.

143 Calculus of a Single Variable II 1 unit
Fall, Spring
Prerequisite: Mathematics 141 or equivalent.
Second half of the standard one-year calculus sequence (see Mathematics 141above). Mathematics 143 covers techniques of integration, applications of the integral, simple differential equations with their associated mathematical models, sequences, and series. Requires a strong working knowledge of algebra, trigonometry, derivatives, and some familiarity with integration, including Riemann sums and the Fundamental Theorem of Calculus. Students with a calculus background who are weak in these areas should elect Mathematics 141. A graphing calculator is required.

210 Introduction to Statistical Analysis 1 unit
Fall, Spring
Prerequisite: Mathematics 141 or its equivalent.
Topics include descriptive statistics, principles of probability, random variables, sampling distributions, point and internal estimation, hypothesis testing, analysis of variance, regression and non-parametric statistics. Substantial use is made of Minitab statistics program on the computer. Students may not receive credit for both Mathematics 109 and 210.

236 Linear Algebra 1 unit
Spring
Prerequisite: Mathematics 143, or Mathematics 239, or permission of instructor.
Vector spaces, matrices, Gauss-Jordan reduction, products, dimension, linear transformations, eigenvalues and eigenvectors, and a selection of applications of linear algebra to other disciplines. Throughout this course, students will develop their skills at mathematical writing and their ability to create mathematical proofs. Properties of equality, logical implication, proof by contradiction, quantification and proof by induction will be illustrated in context.

239 Discrete Structures 1 unit
Fall, Spring
Prerequisite: Mathematics 141.
A survey of discrete mathematics with topics selected from set theory, functions and relations, number theory, combinatorics, graph theory, logic (predicate calculus, quantifiers), introduction to proof techniques, and probability.

245 Multivariate Calculus 1 unit
Fall
Prerequisite: Mathematics 143.
Vectors, inner and cross products, and vector-valued functions including parametric representations of curves and surfaces in space. Partial differentiation, the chain rule, function gradients, implicit differentiation, multivariate optimization, and Lagrange multipliers. Multiple integrals and vector analysis, including divergence and curl of vector fields, as well as the theorems of Green, Stokes, and Gauss.

247 Differential Equations & Linear Algebra 1 unit
Spring
Prerequisite: Mathematics 245.
First-order differential equations and numerical algorithms of Euler and Runge-Kutta. Linear algebraic systems, Gaussian elimination, row-echelon form, matrix algebra, inverses and determinants. Vector spaces, subspaces, linear independence, bases, span, dimension, linear mappings, and function spaces. Second and higher-order linear differential equations. Eigenvectors, eigenvalues, and spectral decomposition methods. First order linear differential systems, including solutions methods using matrix exponentials. Applications focus on problems in physics, chemistry, biology, economics and engineering. Time permitting, additional topics include nonlinear dynamical systems, stability theory, transform theory, and power series solutions.

299 Colloquium in Mathematics & Computer Science I 1/4 unit
Fall, Spring
Offered only on a credit/no credit basis.
Prerequisite: Mathematics 143 or Computer Science 173.
Selected topics in mathematics and computer science as presented by students, departmental faculty and visiting speakers. In addition to submitting written summaries of each presentation, students also write a paper on a mathematics/computer science topic of personal interest.

309 Mathematical Statistics 1 unit
Fall
Prerequisite: Mathematics 236 or 245.
A mathematical study of probability distributions, random sampling, and topics selected from statistical theory: estimation, hypothesis testing, and regression.

310 Applied Mathematical Statistics 1 unit
Spring of odd-numbered years
Prerequisite: Mathematics 309.
A continuation of Mathematics 309. In-depth studies of regression analysis, analysis of variance, experimental design, and nonparametric statistics are included. Topics pertinent to actuarial mathematics are also covered.

316 Numerical Analysis 1 unit
Fall of odd-numbered years
Prerequisites: Mathematics 247 or 236, and Computer Science 171.
Methods of obtaining numerical solutions to mathematical problems. The implementation and error analysis of algorithms are stressed. Topics include: solution of non-linear equations, systems of equations, interpolating polynomials, numerical integration and differentiation, numerical solution to ordinary differential equations, and curve fitting.

326 Operations Research 1 unit
Spring of odd-numbered years
Prerequisites: Mathematics 236 or 247, and Mathematics 245.
An introduction to computational methods in mathematical modeling, including linear programming and Markov chains. Applications in business, economics, and systems engineering. Knowledge of probability will be helpful.

331 Real Analysis 1 unit
Spring
Prerequisites: Mathematics 245 and either Mathematics 236 or 239.
A study of the concepts underlying calculus of a single variable: the completeness property of the real number system, convergence, continuity, properties of elementary functions, the derivative, and the Riemann integral.

335 Abstract Algebra 1 unit
Fall
Prerequisite: Mathematics 236 and 239.
Properties of the integers, real number system and other familiar algebraic entities are viewed abstractly in structures such as groups, semigroups, rings, and fields. Homomorphisms and isomorphisms (functions compatible with the algebraic operations) illuminate the underlying similarities among these structures. Students will develop their skills in mathematical writing and presentations.

342 Geometry 1 unit
Spring
Prerequisites: Mathematics 143 and 239.
The logical foundations of Euclidean geometry, including the axiom systems of Euclid and Hilbert, and their philosophical implications. An introduction to hyperbolic, elliptic, and projective geometry. Students will use software such as Geometer's Sketchpad to illustrate and motivate course topics.

345 History of Mathematics 1 unit
Fall of odd-numbered years
Prerequisite: Mathematics 141.
A study of the history and evolution of mathematical ideas and their significance, from approximately 3500 BCE to the present. Topics include number systems, arithmetic, Euclidean and non-Euclidean geometry, algebra, calculus, probability, number theory, and applied mathematics.

360 Mathematical Modeling 1 unit
Spring of even-numbered years
Prerequisites: Mathematics 236 and Computer Science 171.
An introduction to analytical methods in mathematical modeling, including nonlinear optimization, dynamical systems and random processes. Applications in physics, biology, economics, and systems engineering. Knowledge of probability and statistics will be helpful.

380 Mathematical Physics 1 unit
Spring of even-numbered years.
Prerequisites: Physics 222 or 168, and Mathematics 247, 236, 245 or permission of instructor.
Mathematical methods in physics including vector calculus, transform calculus, tensor analysis, and special functions (viz. Fourier series, Gamma functions, Hermite polynomials, Bessel functions, spherical harmonics, and Laguerre polynomials). Same as Physics 380.

388, 389 Topics 1/2 or 1 unit
Fall, Spring
Prerequisite: Permission of instructor.
Topics chosen to fit departmental interests, such as complex variables, mathematical logic, geometric topology, chaos and fractals, number theory, algebraic coding theory, experimental design, nonparametric statistics, and stochastic processes. Offered on demand.

391, 392 Internship 1/2 or 1 unit
Fall, Spring
Offered on a credit/no credit basis.

399 Colloquium in Mathematics & Computer Science II 1/4 unit
Fall, Spring
Offered only on a credit/no credit basis.
Prerequisite: Mathematics/Computer Science 299 and senior standing.
Selected topics in mathematics and computer science as presented by students, departmental faculty and visiting speakers. In addition to submitting written summaries of each presentation, students take a departmental major assessment examination, and give an oral presentation on a mathematics/computer science topic of personal interest.

401, 402 Seminar 1/2 or 1 unit
Fall, Spring

411, 412 Directed Study 1/2 or 1 unit
Fall, Spring

See the registrar's page for http://www.albion.edu/academics/catalog/departments/math.asp for a printable page of academic information.


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