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Course Descriptions
- MTH 10 Integrated Precalculus/Calculus I [Fall & Winter]
- This course is an introduction to the theory and methods of differential
calculus. Topics included are functions, graphs, limits, continuity
and derivatives. Enrollment is by placement only. Mathematics 10 is
the first of a two course sequence, Mathematics 10-11S. This sequence
covers the material of a standard first term calculus course supplemented
with a review of precalculus mathematics.
- MTH 11S Integrated Precalculus/Calculus II [Winter & Spring]
- Prerequisite: Mathematics 10
This course is an introduction to applications of the derivative and
the theory and applications of the definite integral. Topics included
are the trigonometric functions and their derivatives, applications
of derivatives, antiderivatives, the definite integral and applications
of the integral. This is the second of a two course sequence, Mathematics
10-11S. This sequence covers the material of a standard first term calculus
course supplemented with a review of precalculus mathematics.
- MTH 11 Analytic Geometry and Calculus I [Fall, Winter & Spring]
- Prerequisite: A sufficiently high score on the placement test
The first course in the standard calculus sequence. Introduction to
the theory, methods, and applications of differential calculus and an
introduction to the definite integral. Topics include algebraic and
trigonometric functions, limits and continuity, rules for differentiation,
applications of the derivative, antiderivatives, and the definition
and basic properties of the definite integral.
- MTH 12 Analytic Geometry and Calculus II [Fall, Winter & Spring]
- Prerequisite: Mathematics 11
The second course in the standard calculus sequence.Included are an
introduction to the logarithmic and exponential functions, the applications
of the definite integral, techniques of integration, indeterminate forms,
improper integrals, numerical methods and infinite series.
- MTH 13 Vectors and Matrices [Fall, Winter & Spring]
- Prerequisite: Mathematics 12
Introduction to the theory of vectors and matrices. Among the topics
included are: vectors, vector operations, the geometry of Euclidean space,
systems of equations, matrices, matrix operations, special transformations,
eigenvalues, and applications of matrix theory.
- MTH 15 Ideas in Mathematics [Fall, Winter & Spring]
- An examination of the ideas, concepts, and paradigms which have had
significant influence on the growth of modern mathematical thought,
with an emphasis on an appreciation for the creative side of mathematics
and the fundamental role it has played in the development of modern
civilization. Topics will be drawn from across the spectrum of mathematical
thought, and will be treated from a historical and cultural as well
as mathematical perspective.
- MTH 16 Finite Mathematics [Fall, Winter & Spring]
- Mathematical topics applicable to the social sciences and business
selected from the following: logic, set theory, combinatorics, statistics,
matrix algebra, linear programming, Markov chains, graph theory, and
mathematics of finance. A student cannot receive credit for this course
after credit has been received for Mathematics 28 or any Mathematics
course numbered above 33.
- MTH 21 Vector Calculus [Spring]
- Prerequisite: Mathematics 13
Introduction to multivariate and vector calculus. Topics include vector functions and the differential and integral calculus of functions of several variables including Green's Theorem and Stokes' Theorem.
- MTH 22 Differential Equations [Fall & Winter]
- Prerequisite: Mathematics 13
Introduction to the theory, methods, and applications of ordinary differential
equations, including first- and higher-order differential equations,
series solutions, systems, approximate methods, Laplace transforms,
and phase plane analysis.
- MTH 28 Introduction to Discrete Mathematics [Fall]
- Prerequisite: Mathematics 12 or consent of instructor
Introduction to the main ideas and proof techniques of discrete mathematics.
Among the topics covered are mathematical logic, relations, functions,
partitions, recursion, induction, combinatorial principles, inclusion/exclusion,
enumeration, and introductory graph theory (trees, connectivity, planarity,
colorings, etc.).
- MTH 30 Introduction to Statistics [Spring]
- Prerequisite: Mathematics 11 or 16, or consent of instructor
Non-theoretical, precalculus course in elementary probability and statistics.
Counting problems, probability, various distributions, random variables,
estimation, hypothesis testing, regression and correlation, analysis
of variance, and nonparametric methods. A student cannot receive credit
for this course and Mathematics 47 or Economics 25.
- MTH 31 Mathematics for Elementary School Teachers I [Fall]
- Logic, sets, relations, deductive reasoning, numeration systems,
the systems of whole numbers and integers, computational algorithms,
and methodology appropriate for teaching this content in elementary
school (K-8).
- MTH 32 Mathematics for Elementary School Teachers II [Winter]
- Prerequisite: Mathematics 31
Elementary number theory, fractions, decimals, percent, applications
of percent, simple probability, descriptive statistics, and methodology
appropriate for teaching this content in elementary school (K-8).
- MTH 33 Mathematics for Elementary School Teachers III [Spring]
- Prerequisite: Mathematics 32
Introductory geometry, construction, congruence, similarity, measurement
(including the metric system), an introduction to Logo turtle graphics,
and methodology appropriate for teaching this content in elementary
school (K-8).
- MTH 34 Linear Algebra and Matrix Theory [Spring, Odd Numbered Years]
- Prerequisite: Mathematics 13, 28
Study of finite dimensional real vector spaces, linear transformations,
determinants, inner product spaces, eigenvalues and eigenvectors.
- MTH 35 Number Theory [Winter, Even Numbered Years]
- Prerequisite: Mathematics 28 or consent of instructor
Introduction to the arithmetic properties of the integers including
divisibility, congruences, diophantine equations, primes and their distribution,
quadratic forms and quadratic reciprocity. Additional topics will be
chosen from continued fractions, cryptography, partitions, elliptic
curves, modular forms and number fields.
- MTH 36 Modern Geometry [Fall, Odd Numbered Years]
- Prerequisite: Mathematics 28 or consent of the instructor
Development of Euclidean and non-Euclidean geometries. Topics include
axiom systems, models, congruence theorems, parallel postulates, and
the philosophical and historical background to geometry.
- MTH 37 Probability [Winter]
- Prerequisite: Mathematics 21
Calculus-based course in probability,covering counting, discrete and
continuous probability, random variables, important probability distributions,
joint distributions, expectation, moment generating functions, and applications
of probability.
- MTH 38 Combinatorics and Graph Theory [Winter, Odd Numbered Years]
- Prerequisite: Mathematics 28
A study of the primary methods and fundamental ideas of combinatorics and graph theory. Topics covered include generating functions, set partitions, recurrence relations, inclusion-exclusion, trees, graph connectivity, independence, and graph colorings. Additional topics will be chosen from Ramsey theory, set systems, planarity, directed graphs, matchings, and Hamiltonian and Eulerian graphs.
- MTH 39 Complex Variables [Spring, Even Numbered Years]
- Prerequisite: Mathematics 21
Study of the complex plane and the calculus of functions of a complex variable. Topics to be considered include the algebra and geometry of complex numbers, limits and derivatives of functions of a complex variable, the Cauchy-Riemann equations, contour integrals, Taylor and Laurent series, and residues.
- MTH 40 Mathematical Models and Applications [Fall, Even Numbered Years]
- Prerequisites: Mathematics 21, 22
A selection of mathematical models using various continuous and discrete methods and having applications in business and the social and biological sciences. Included are ecological models, epidemic models, Richardson's arms race model, and cultural stability models. Other topics discussed are linear programming, voting problems, and Markov chains.
- MTH 41 Real Analysis [Fall, Even Numbered Years]
- Prerequisite: Mathematics 28
A theoretical introduction to some of the basic ideas of real analysis:
real numbers and the topology of the real line, sequences and series
of real numbers, limits of functions, continuity, uniform continuity,
differentiation, the Riemann integral, and sequences and series of functions.
- MTH 42 Topics in Analysis [Spring, Odd Numbered Years]
- Prerequisite: Mathematics 41 or consent of the instructor
An in-depth investigation of selected topics in analysis.
- MTH 43 Modern Algebra [Fall, Odd Numbered Years]
- Prerequisites: Mathematics 28
A theoretical introduction to some of the basic ideas of modern abstract
algebra. Included is a study of groups, rings, domains, polynomial rings
and fields as well as an investigation of their substructures and of
the fundamental homomorphism theorems.
- MTH 44 Topics in Algebra [Spring, Even Numbered Years]
- Prerequisite: Mathematics 43 or consent of the instructor
An in-depth investigation of selected topics in abstract algebra.
- MTH 46 Topology
- Prerequisites: Mathematics 28
Introduction to concepts in topology including the following: topological
spaces, metric spaces, continuity, homeomorphisms, neighborhoods, closed
sets and closure, basis and sub-basis for a topology, subspaces, product
spaces, connectivity, compactness, and separation axioms.
- MTH 47 Mathematical Statistics [Spring]
- Prerequisite: Mathematics 37
Calculus-based course in statistics covering sampling, estimation, hypothesis
testing, chi-square tests, regression, correlation, analysis of variance,
experimental design, and nonparametric statistics.
- MTH 55 Teaching Mathematics in Grades 9-12
- Prerequisites: Education 11, 20, 21
(Same as Education 55) Teacher candidates become reflective practitioners
in the development and delivery of a well-designed, standards-based
mathematics curriculum. Topics include mathematics curriculum in the
secondary school, instructional strategies, performance assessment and
resource evaluation focusing on technology. Students are expected to
participate in field work in local mathematics classrooms. To be taken
winter term of the senior year concurrently with Education 50/Education
02.
- MTH 80 Directed Independent Study
- Study of an area of mathematics of interest to the student that is
not part of one of the listed courses. The student must choose a faculty
member to direct the study and, together with this faculty member, prepare
a description of the material to be covered and submit it to the department
chair for approval.
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