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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