May 01, 2024  
2019-2020 Academic Catalog 
    
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2019-2020 Academic Catalog [ARCHIVED CATALOG]

Course Descriptions

Course Numbering System

The following lists include all courses normally offered at Albion College. However, not all courses are offered every year. When possible, courses offered in alternate years are designated. For details, students should consult the Class Schedule for each semester, available online at: www.albion.edu/registrar. The College reserves the right to add or withdraw courses without prior announcement, as conditions may require.

Unless otherwise stated, 100 level courses are intended for freshmen, 200 level for sophomores, 300 and 400 level for juniors and seniors.

A list of courses which meet the core and category requirements, organized by departments, is available online at www.albion.edu/registrar.

Further information may be obtained at the Registrar’s Office in the Ferguson Student, Technology, and Administrative Services Building.
 

Mathematics

Initial course placements in mathematics and computer science are generally determined by the Mathematics Placement Test. After students take their first course, they must take courses in sequence as determined by the departmental prerequisites. Any exceptions must be approved by the course instructor and department chair.
  

  • MATH 100: Mathematics Essentials

    (1 Unit)
    Prerequisite:  Appropriate score on the mathematics placement assessment and permission of department.
    A review of the basics from elementary algebra; absolute value equations and inequalities; radical and rational exponents; completing the square; the discriminant; quadratic inequalities; equations of lines; systems of equations; functions, polynomials and factoring, inverses and their graphs; word problems; exponential and logarithmic functions. Emphasizes simplifying expressions, solving equations, and graphing functions, including linear, quadric, polynomial, rational, radical, exponential and logarithmic. Problem solving and mathematical modeling will be integrated throughout.  A minimum grade of 2.0 is required in any mathematics course used as a prerequisite for another mathematics course. Staff
  

  • MATH 104: Mathematics for Elementary Teachers

    (1 Unit)
    Prerequisite: MATH 100   or placement evaluation at the MATH 120   level or higher.
    Priority given to students in the elementary education program. An investigation of mathematics (arithmetic, geometry, algebra, problem solving) for elementary school teachers. Topics are selected 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. Emphasizes doing mathematics, using manipulatives, and developing intuition and problem-solving skills.  Laboratory. Bollman.
  

  • MATH 119: Finite Mathematics for Decision Making

    (1 Unit)
    Prerequisites: 2.0 or higher in Math 100 or appropriate score on the mathematics placement assessment.
    An introduction to discrete mathematics. Applications are drawn from diverse areas including biological sciences, economics, political science and personal finance. Topics typically include graph theory, management science, statistics, the mathematics of social choice, game theory and the logical foundations of mathematics. Investigation and creation of mathematical models. Intended for non-majors. Staff.
  

  • MATH 120: College Algebra

    (1 Unit)
    Prerequisites: 2.0 or higher in MATH 100   or equivalent, or appropriate score on the mathematics placement assessment.
    A modern, unified approach to algebra 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 are normally covered. Emphasizes the use of graphing calculators and the use of mathematics as a problem-solving tool. Covers applications in natural science, social science and business. Together with MATH 127  , serves as a preparation for calculus. Well-prepared students who already have a strong working knowledge of algebra, trigonometry and logarithms should elect MATH 141   in place of MATH 120. A graphing calculator is required. Not open to students who have completed MATH 125  .  A minimum grade of 2.0 is required in any mathematics course used as a prerequisite for another mathematics course. Staff
  

  • MATH 123: Mathematics for the Liberal Arts

    (1 Unit)
    Prerequisite: Permission of department.
    A study of selected topics in mathematics drawn from among algebra, geometry, statistics, probability, discrete mathematics, and other fields of mathematics as determined by the instructor. Staff.
  

  • MATH 125: Precalculus

    (1 Unit)
    Prerequisite: 2.0 or higher in Math 100 or appropriate score on teh mathematics placement assessment.
    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) are normally covered. Emphasizes the use of graphing calculators and the use of mathematics as a problem-solving tool. Covers applications in natural science, social science and business. Serves as a preparation for calculus. Well-prepared students who already have a strong working knowledge of algebra, trigonometry and logarithms should elect MATH 141  in place of Mathematics 125. A graphing calculator is required. Not open to students who have completed Math 120. Staff.
  

  • MATH 127: Trigonometry

    (.5 Unit)
    Prerequisites: 2.0 or higher in MATH 120   or equivalent, or appropriate score on the mathematics placement assessment.
    Topics covered include the definition of trigonometric functions, graphs of the trigonometric functions, trigonometric identities, solving trigonometric equations, utilizing polar coordinates, and vector applications & operations. A minimum grade of 2.0 is required in any mathematics course used as a prerequisite for another mathematics course. Staff
  

  • MATH 141: Calculus of a Single Variable I

    (1 Unit)
    Prerequisite: 2.0 or higher in MATH 120   (College Algebra) AND concurrent enrollment in MATH 127   (Trigonometry); or 2.0 or higher in MATH 125   (Precalculus); or appropriate score on the mathematics placement assessment.
    MATH 141 and MATH 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. Second half of the standard one-year calculus sequence (see MATH 141 above). MATH 141 covers limits, continuity, derivatives and a brief introduction to integration, as well as applications to problems in related rates, optimization, solid geometry and elementary mechanics. Requires a strong working knowledge of algebra and trigonometry. Students who are weak in these areas should elect MATH 125 . A graphing calculator is required. A minimum grade of 2.0 is required in any mathematics course used as a prerequisite for another mathematics course. Staff.
  

  • MATH 143: Calculus of a Single Variable II

    (1 Unit)
    Prerequisite: MATH 141  or permission of department.
    Mathematics 143 covers techniques of integration, applications of the integral, simple differential equations with their associated mathematical models, and 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 MATH 141 . A graphing calculator is required. A minimum grade of 2.0 is required in any mathematics course used as a prerequisite for another mathematics course. Staff.
  

  • MATH 209: An Introduction to Statistics

    (1 Unit)
    Prerequisite: 2.0 or higher in MATH 100   or appropriate score on the mathematics placement assessment.
    Statistics is the art/science of collecting and interpreting data. Topics include probability, probability distributions which include the binomial and normal distributions, the central limit theorem, sampling distributions, confidence interval estimation, and hypothesis testing. Students will then advance to linear regressions, goodness-of-fit tests, and analysis of variance. Emphasis is placed on multiple applications in the life and social sciences. A minimum grade of 2.0 is required in any mathematics course used as a prerequisite for another mathematics course. Anderson, Bollman.
  

  • MATH 239: Discrete Structures

    (1 Unit)
    Prerequisite: MATH 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.  A minimum grade of 2.0 is required in any mathematics course used as a prerequisite for another mathematics course. Kamischke.
  

  • MATH 245: Multivariate Calculus

    (1 Unit)
    Prerequisite: MATH 143 .
    Vectors, inner and cross products, and vector-valued functions including parametric represetations of curves and surfaces in space.  Partial differentiation, the chain rule, function gradients, implicit differentiation, multivariate optimization, Lagrange multipliers, multiple integrals and vector analysis, including divergence and curl of vector fields, as well as the theorems of Green, Stokes and Gauss. Mason.
  

  • MATH 247: Differential Equations and Linear Algebra

    (1 Unit)
    Prerequisite: MATH 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. Additional topics may include nonlinear dynamical systems, stability theory, transform theory and power series solutions. Mason.
  

  • MATH 250: Problem Solving Seminar

    (1/4 Unit)
    Prerequisites: MATH 141  and permission of instructor
    An examination of problem-solving strategies from all areas of mathematics, with particular emphasis on mathematics competition problems. Students will participate in the Michigan Autumn Take-Home Challenge and William Lowell Putnam Mathematical Competition. Fall semester only; may be repeated for credit up to one full unit of credit. CR/NC only (Bollman)
  

  • MATH 257: Mathematics of the Gaming Industry

    (1/4 Unit)
    Permission of instructor.  Open to department majors and minors only.
    A detailed study of probability as applied to games of chance.  Students will have the opportunity to compare theory and practice through classroom experiments and travel to casinos.  CR/NC only.  Bollman
  

  • MATH 275: Introduction to Solid Mechanics

    (1 Unit)
    Prerequisites: PHYS 167  and PHYS 168 ; MATH 245 .
    Statics: Forces, moments and couples; equilibrium of particles and rigid bodies; trusses and frames; distributed loads; Friction. Mechanics: Stress/strain, classification of material behavior, generalized Hooke’s law. Engineering applications: Axial loads, torsion of circular rods and tubes, bending and shear stresses in beams, deflection of beams, combined stresses, stress and strain transformation, Mohr’s circle, elastic stability/buckling of columns. A minimum grade of 2.0 is required in any mathematics course used as a prerequisite for another mathematics course. Same as Physics 275. Same as Physics 275. Mason.
  

  • MATH 299: Colloquium in Mathematics and Computer Science

    (1/4 Unit)
    Prerequisite: MATH 143  or CS 173 .
    Selected topics in mathematics and computer science as presented by students, departmental faculty and visiting speakers. Requirements include written summaries of each presentation and a paper on a mathematics/computer science topic of personal interest. Same as CS 299 . Staff.
  

  • MATH 309: Mathematical Statistics

    (1 Unit)
    Prerequisite: MATH 245 .
    MATH 247  is recommended. A mathematical study of probability distributions, random sampling, and topics selected from statistical theory: estimation, hypothesis testing and regression. A minimum grade of 2.0 is required in any mathematics course used as a prerequisite for another mathematics course. Anderson.
  

  • MATH 311: Regression and Time Series Models

    (1 Unit)
    Covers two topics in detail: multiple linear regression analysis and time series analysis. Inherent to both topics: parsimonious linear models, parameter estimation, diagnostic checking, and forecasting. Uses the matrix approach for multiple linear regression, and the Box-Jenkins methodology for constructing autoregressive-integrated moving average (ARIMA) models for time series analysis. Employs the statistical package MINITAB for analyzing all real-world data sets. Anderson.
  

  • MATH 313: Financial Mathematics for Actuaries

    (1 Unit)
    MATH 209   or MATH 309   MATH 247  
    Introduction to mathematics of financial derivatives in discrete time.  Risk-neutral/arbitrage-free modeling of risky securities including options, forwards, futures, and swaps.  Emphasis on single and multi-period Arrow-Debreu models and discrete-time stochastic processes with applications to actuarial mathematics. Mason
  

  • MATH 316: Numerical Analysis

    (1 Unit)
    Prerequisites: MATH 247  and CS 171 .
    Methods of obtaining numerical solutions to mathematical problems. Stresses the implementation and error analysis of algorithms. 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. Offered in alternate years. Same as CS 316 . Mason.
  

  • MATH 326: Operations Research

    (1 Unit)
    Prerequisites: MATH 247 .
    An introduction to computational methods in mathematical modeling including linear programming and Markov chains. Applications in business, economics and systems engineering. Knowledge of probability is helpful. Offered in alternate years. Same as CS 326 . Mason.
  

  • MATH 331: Real Analysis

    (1 Unit)
    Prerequisites: MATH 245  and MATH 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. Bollman.
  

  • MATH 333: Complex Analysis

    (1 Unit)
    Prerequisites: MATH 239  and MATH 245 .
    An introduction to complex variable theory. Specific topics to be covered include elementary and analytic functions, differentiation and integration in the complex plane, series representations, residues and poles, transform theory, and conformal mapping. Offered in alternate years. Bollman.
  

  • MATH 335: Abstract Algebra

    (1 Unit)
    Prerequisites: MATH 239  and MATH 247 .
    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. Bollman.
  

  • MATH 342: Geometry

    (1 Unit)
    Prerequisites: MATH 143  and MATH 239 .
    The logical foundation of Euclidean geometry, including the axiom systems of Euclid and Hilbert, and their philosophical implications. An introduction to hyperbolic, elliptic and projective geometry. Employs software such as Geometer’s Sketchpad to illustrate course topics. Bollman.
  

  • MATH 345: History of Mathematics

    (1 Unit)
    Prerequisite: MATH 141 .
    A study of the history and evolution of mathematical ideas and their significance, from approximately 3500 B.C.E. to the present. Topics include number systems, arithmetic, Euclidean and non-Euclidean geometry, algebra, calculus, probability, number theory and applied mathematics. Offered in alternate years. Bollman.
  

  • MATH 349: Advanced Linear Algebra

    (1 Unit)
    Prerequisites: MATH 239  and MATH 247 .
    A continued study of linear algebra as begun in MATH 247 . Topics may include abstract vector spaces, dimension, normed linear spaces, inner product spaces, canonical forms, unitary and Hermitian matrices, factorization, eigenvector analysis, and infinite-dimensional spaces. Offered in alternate years. Bollman.
  

  • MATH 358: Foundations of Computing

    (1 Unit)
    Prerequisites: MATH 239   and CS 171  
    The theoretical underpinnings of computer science: models of computation including automata, Turing machines, circuits, the Chomsky language hierarchy, Church’s thesis, computable and noncomputable functions, recursive and recursively enumerable sets, reducibility and introduction to complexity theory. Same as CS 358  . Jordon.
  

  • MATH 360: Mathematical Modeling

    (1 Unit)
    Prerequisites: MATH 247  and CS 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 is helpful. Same as CS 360 . Mason.
  

  • MATH 368: Topology

    (1 Unit)
    Prerequisites: MATH 239  and MATH 245 .
    An introduction to the basic concepts of point set topology. Fundamental concepts of topological spaces including open and closed sets, limit points, continuous functions, as well as the product, subspace, metric, and quotient topology. Connectedness and compactness with applications to the real line. Countability and separation axioms including Hausdorff, Regular, and Normal spaces. Urysohn’s Lemma and Metrization Theorem. Tychonoff’s Theorem. Topics from algebraic topology if time permits. Urysohn’s Lemma and Metrization Theorem. Tychonoff’s Theorem. Topics from algebraic topology if time permits. Mason, Bollman.
  

  • MATH 370: Partial Differential Equations

    (1 Unit)
    Prerequisites: MATH 239  and MATH 247 .
    MATH 331  recommended. A study of the theory and applications of partial differential equations (PDEs). Linear and nonlinear PDEs, including quasilinear first order equations, conservation laws, discontinuous solutions, classification of PDEs, wave propagation in multiple space dimensions, Fourier analysis and separation of variables, Sturm-Liouville theory, fundamental solutions for equations of parabolic and elliptic type, including the maximum principle. Applications in biology, chemistry, engineering and physics. Offered in alternate years. Mason.
  

  • MATH 380: Mathematical Physics

    (1 Unit)
    Same as PHYS 380 . Staff.
  

  • MATH 399: Colloquium in Mathematics and Computer Science

    (1/4 Unit)
    Prerequisites: MATH 299  and senior standing.
    Selected topics in mathematics and computer science as presented by students, departmental faculty and visiting speakers. Requirements include written summaries of each presentation, a departmental major assessment examination and an oral presentation on a mathematics/computer science topic of personal interest. Offered only on a credit/no credit basis. Same as CS 399 . Staff.