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Albion
College
Mathematics and Computer Science
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Mathematics
104 Mathematics for Elementary Teachers
1 unit
Spring
Prerequisites: Three years of college-preparatory mathematics (or its
equivalent) and permission of the department. 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
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.
219 Elementary Differential Equations
1 unit
Spring
Prerequisite: Mathematics 143 or equivalent.
An introduction to ordinary differential equations with a strong emphasis on
applications. First-order equations, second-order linear equations, power
series, Laplace transforms, numerical methods and linear systems.
Applications in physics, chemistry, biology, economics and engineering. May
be elected by students who have completed a high school advanced placement
calculus course equivalent to Mathematics 143.
236 Linear Algebra
1 unit
Fall, 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
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 or permission of instructor.
Topics include vectors, surfaces in space, partial differentiation,
optimization, Lagrange multipliers, multiple integrals, line integrals, and
surface integrals.
309 Mathematical Statistics
1 unit
Fall of even-numbered years
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 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.
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 of even-numbered years
Prerequisites: Mathematics 143 and
236.
The logical foundations of Euclidean geometry. An introduction to other
geometries: projective, affine, etc. Geometrical transformations with
emphasis on their application to computer graphics. Selected topics.
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
219, 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.
401, 402 Seminar
1/2 or 1 unit
Fall, Spring
411, 412 Directed Study
1/2 or 1 unit
Fall, Spring
Computer Science
151 Survey of Computing
1 unit
Fall, Spring
Prerequisite: Three years of high school mathematics or permission of
instructor.
Provides a basic knowledge of computers and the experience necessary to use
computers effectively in the solution of problems. Students will do
programming in a high-level programming language such as BASIC or Pascal, as
well as use specialized programs such as word processors, data base managers,
and electronic spreadsheets. Additional topics will be selected from computer
hardware and software components, problem-solving and algorithms, the method
of step-wise refinement, program debugging, graphics and animation,
simulations and games, the Internet, Boolean expressions, networks, artificial
intelligence, and the social consequences of computers. Not open to students
who have had Computer Science 171.
171 Introduction to Computer Science I
1 unit
Fall, Spring
Prerequisite: Mathematics 125 (or equivalent); or
permission of the instructor.
Designed to be the first computer science course taken by students in
mathematics and science, as well as by those wishing to concentrate in
computer science. Topics include fundamentals of computation and algorithmic
problem solving, data types, procedures, control structures, structured data
types (arrays, records, sets, simple linked lists and trees), and
applications. A high-level programming language is also studied. Students
with a year or more of computer science at the secondary level may be
qualified for Computer Science 173.
173 Introduction to Computer Science II
1 unit
Fall, Spring
Prerequisite: Computer Science 171 or permission of the
instructor.
A continuation of Computer Science 171.
Emphasis is on abstract data types (stacks,
queues, lists, strings, trees, graphs, etc.) and analysis of algorithms.
Other topics include pointers, recursion, searching and sorting, simulation,
and an introduction to some of the advanced areas of computer science: e.g.,
computer organization, compilers and operating systems. Students also will
refine their programming skills in a high-level programming language.
256 Practicum in Programming Languages
1/4 unit
Fall, Spring
Prerequisite: Computer Science 171 or permission of the instructor.
Designed to teach an additional computer
language beyond those currently used in the computer science courses. The
emphasis will be on writing and debugging programs that use the special
features of the language. FORTRAN and C are the languages that have been
taught most recently. Special sections of this course have been devoted to
developing problem-solving skills in computer programming.
271 Computer Understanding of Human Languages
1 unit
Spring of even-numbered years
Prerequisite: Ability to program in a high-level computer language.
A case study in artificial intelligence focusing on computer understanding
of natural human languages. Topics include the logic programming language
Prolog, simple models of machine learning, parsing English sentences, using
a database of facts to determine the meaning of an ambiguous sentence, and
computer translation of natural languages.
280 Microcomputer Programming and Circuit Design
1/2 unit
Fall of even-numbered years
Prerequisite: Physics 115 or Mathematics 141, or
Computer Science 171, or permission of instructor.
Introduction to programming microcomputers at the machine-code level and the
design and construction of electronic circuitry required to connect
microcomputers to external devices for control and/or data acquisition.
Topics include number systems, computer architecture and arithmetic,
character coded data, input/output and analog-to-digital conversion. Lecture
and laboratory.
316 Numerical Analysis
1 unit
Fall of odd-numbered years
Prerequisites: Mathematics 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.
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.
352 Data Structures and Algorithms
1 unit
Fall of odd-numbered years
Prerequisite: Computer Science 173 and Mathematics 239.
This course focuses on the design and efficiency of algorithms.
Topics include algorithmic paradigms, algorithm design and analysis,
and advanced data structures (stacks, queues, trees, graphs, and the like).
Proof techniques at the level of Mathematics 239 will be used.
354 Computer Organization and Systems
1 unit
Spring of even-numbered years
Prerequisite: Computer Science 173.
Topics include hardware organization, assembly and system-level programming,
input-output and secondary storage devices, control of input-output devices,
digital logic, hardware control and microprogramming, multiprogramming and
multiprocessors. Programming tools and techniques are also discussed with
emphasis on their application in assembly language.
356 Programming Languages
1 unit
Fall of even-numbered years.
Prerequisite: Computer Science 173.
Topics include language definition structure, data types and structures,
control structures and data flow, run-time considerations, interpretive
languages, lexical analysis and parsing, enhancements. Students will review
the Pascal programming language in depth. They will compare and contrast it
with other major procedural languages such as FORTRAN, Algol. Certain special
purpose languages will also be examined: e.g., Prolog, Icon, Logo.
358 Foundations of Computing
1 unit
Spring of odd-numbered years.
Prerequisite: Computer Science 173 and Mathematics 239.
The theoretical underpinnings of computer science. Topics will be selected
from automata, regular expressions, language syntax, context-free grammars,
Backus-Naur form, parsing, language processors, compilers, interpreters,
Turing machines, and the halting problem.
360 Mathematical Modeling
1 unit
Spring of even-numbered years.
Prerequisites: Mathematics 219 and
245.
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.
388, 389 Topics
1/2, 1 unit
Fall, Spring
Prerequisite: Permission of instructor.
Topics in computer science such as recursive function theory, computational
complexity, formal languages and algorithms.
391, 392 Internship
1/2, 1 unit
Fall, Spring
Offered on a credit/no credit basis.
411, 412 Directed Study
1/2, 1 unit
Fall, Spring
Link to the Albion College home page.
Link to the Mathematics Department home page.
Modified January 3, 1997, by David Reimann
Modified October 16, 2001, by Robert Messer