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Chair: Walter Czarnec
Professors: Walter Czarnec, Thomas Koshy, Kenneth
Preskenis, Sonja Sandberg
Associate Professors: Anita Goldner, Martin
Price, Mohammad Salmassi
Assistant Professors: Joyce Cutler, Eileen
Lee, Sarah
Mabrouk
Computing Facilities Include:
Novell LAN (Netware 2.15) with 60
PCs
Four (4) networked UNIX
workstations-5 M
Amiga 3000UXs
running UNIX System V release 4
The General Education Requirement
All students
must satisfy a general education requirement consisting of twelve (12) courses
(see page 32 of this catalog.) General Education Goal 2 (Quantitative) is
covered in courses taken by Mathematics majors, and is therefore considered
fulfilled through the major.
Placement Testing
Each incoming student must take
a placement examination in mathematics, which is administered during orientation
for new students. Shown below are additional dates and times for the
examination during the 2000-2001 academic year, to be given in the Center for
Academic Support and Advising (CASA).
| Tuesday, September 4,
2001 |
10:30am |
| Tuesday, September 4, 2001 |
4:30 pm |
| Tuesday, October 23, 2001 |
4:30 pm |
| Wednesday, October 24, 2001 |
1:30 pm |
| Monday, January 23,
2002 |
4:30 pm |
| Wednesday, March 27, 2001 |
1:30 pm |
| Thursday, March 28, 2002 |
4:30 pm |
MATHEMATICS MAJOR
All students must complete the following seven (7) core
courses:
43.219 Calculus
I
43.220 Calculus
II
43.221 Calculus
III
43.226 Linear
Algebra and Applications
43.310 Number
Theory
43.317
Introduction to Higher Geometry
43.319 Modern
Algebra
One (1) computer science course
One (1) course in probability and
statistics
Three (3) electives in mathematics,
numbered at the 200 level or above, with at least one numbered at the 300 level
or above.
PROGRAMS IN MATHEMATICS
GENERAL (MAG):
In addition to the twelve (12)
core requirements above, each student must complete:
43.222
Differential Equations
43.427
Real Analysis
Six (6) electives from mathematics, physics,
computer science, or an approved minor
MATHEMATICS WITH MINOR IN SECONDARY EDUCATION
(MAT):
In addition to the twelve (12) core requirements above, each
student must complete:
43.222
Differential Equations
43.427
Real Analysis
42.200
Psychology of Development
14.200
Education in American Society with Field Study
I
14.315
Professional Preparation and Field
14.316
Study II: Methods, Special Education & Technology: High
School/Middle/// School (Credit - two courses)
14.410
Student Teaching Practicum and Seminar I- Secondary (Credit-two courses)///
14.411
Student Teaching Practicum and Seminar II - Secondary (Credit-two
courses)
Note: Mathematics Department prerequisites for 14.315
Professional Preparation and Field Study II - High School and 14.316
Professional Preparation and Field Study II - Middle School are completion
of:
All required mathematics courses except:
43.319
Modern Algebra
43.427
Real Analysis
Prerequisites for 14.410-411 Student Teaching Seminar and
Practicum I-II - High School and 14.414-15 Student Teaching Seminar and
Practicum I-II - Middle School are completion of all department requirements,
plus 14.315 Professional Preparation and Field Study II - High School or 14.316
Professional Preparation and Field Study II - Middle School, depending on the
level.
COORDINATE MAJOR IN EARLY CHILDHOOD OR ELEMENTARY
EDUCATION (MAE)
I. Mathematics requirements
In addition to the twelve (12) core requirements listed
above, each student must complete:
43.110 College Mathematics I
It is strongly recommended that students select 43.201
Intuitive Geometry and 43.301 Problem Solving and Modeling in Mathematics as two
of their three mathematics electives among the core courses.
II. Choose A or B
A. Coordinate Major in Early Childhood Education
(Pre-K - Grade 3 Certification)
14.200
Education in American Society with Field Study I (Gen.Ed.)
42.200
Psychology of Development (Gen.Ed.)
14.320
The Young Child: Emerging Literacy with Field Study II
14.374
Early Childhood Curriculum: Mathematics and Science with Field Study III
14.376
Early Childhood Curriculum: Reading, Social Studies, and Special Needs
The Professional Semester (four courses):
14.431
Early Childhood Professional Practicum A (Credit—two courses)
14.432
Early Childhood Professional Practicum B (Credit—two courses)
B. Coordinate Major in Elementary Education (Grades 1 -
6 Certification)
14.200
Education in American Society with Field Study I (Gen.Ed.)
42.200
Psychology of Development (Gen.Ed.)
14.322
The Child and Literacy with Field Study II
14.341
Elementary Curriculum: Mathematics with Field Study III
14.346
Elementary Curriculum: Science, Social Studies and Special Needs
The Professional Semester (four courses):
14.437
Elementary Professional Practicum A (Credit—two courses)
14.438
Elementary Professional Practicum B (Credit—two courses)
Note: 14.200 and
42.200
may be used to fulfill the college requirement for general education.
Double Major in Mathematics and Computer
Science
Required Mathematics Courses
43.219-1
Calculus I-Calculus III
43.222
Differential Equations
43.226
Linear Algebra and Applications
43.292
Discrete Mathematics I
43.313
Numerical Methods
43.323
Advanced Calculus
43.333
Operations Research and Modeling
43.335
Algebraic Structures I////
43.348-9
Mathematical Statistics I-II
Required Computer Science Courses
63.152
Computer Science I Using C and 63.252 Computer
Science II with Advanced C or
63.259
Object Oriented Programming Using C++
63.261
Computer Organization and Assembly Language Programming
63.271
Data Structures
63.355
Computer Architecture
63.362
Software Engineering
63.465
Operating Systems
63.477
Computer Networking
Required Physics Course
53.321
Digital Electronics
Computer Science Elective
One (1) course in computer science,
numbered 300 or above.
MINOR IN MATHEMATICS (5 courses)
43.219
Calculus I and four (4) additional credit-bearing mathematics courses approved
by the student's advisor.
MINOR IN STATISTICS (5 courses)
Required courses:
43.117
Introduction to Statistics
43.307
Intermediate Statistics
43.308
Applied Statistical Data Processing
Plus two (2) electives from:
12.470
Applied Econometrics for Economics and Business
42.251
Research Methods in Psychology I
42.351
Research Methods in Psychology II
43.215
Finite Mathematics
43.348
Mathematical Statistics I
43.349
Mathematical Statistics II
63.___
A computer science course (only one computer science course may be used as an
elective towards a minor in statistics).
Note: The courses selected for the minor must be from
a department different from the student’s major.
Mathematics Courses Appropriate for General
Education (Gen.Ed.)
* indicates that course has prerequisite.
Course Descriptions
from the 2001-2002 Undergraduate College
Catalog
43.095 General Mathematics (no course credit)
A non-credit course covering the essentials of
high school algebra. Time will be spent on common arithmetic difficulties and
elementary metric geometry. Prerequisite: Permission of the Mathematics
Department.
43.110 College Mathematics I (Gen.Ed. Goal 2)
An exploration of numbers, their
representations, relationships, and uses; arithmetic; elementary set theory;
basic logic; geometry; measurement; probability; and statistics. This course
offers a college-level treatment of content areas of interest to prospective
early childhood and elementary teachers. Problem-solving and the communication
of mathematical ideas, both verbally and algebraically, are woven throughout the
course. Note: Students may not receive credit for both 43.110 and 43.113
Introduction to College Mathematics. Prerequisite: Satisfactory score on the
mathematics placement examination or permission of the Mathematics
Department.
43.117 Introduction to Statistics (Gen.Ed. Goal 2)
An introduction to the discipline of
statistics, emphasizing both statistical thinking and its application to
analyzing data. Topics include sampling, design of experiments, organizing and
exploring data, probability distributions such as the normal distribution,
sampling distributions, hypothesis testing and confidence intervals, correlation
and regression. Students are expected to express results of statistical
procedures in ordinary non-technical language. Real world applications of
statistical topics are emphasized throughout the course. Prerequisite:
Satisfactory score on the mathematics placement examination or permission of the
Mathematics Department.
43.119 Mathematics and Its Applications (Gen.Ed. Goal 2)
A study of mathematics through applications.
Topics include sets, an introduction to formal logic, functions and graphs,
geometry, probability, statistics, matrices, linear programming, and the theory
of interest. This course is recommended for students who do not require 43.110
College Mathematics I, 43.117 Introduction to Statistics, or 43.123 College
Algebra for their major. Prerequisite: Satisfactory score on the mathematics
placement examination or permission of the Mathematics Department.
43.120 College Mathematics II
A continuation of 43.110 College Mathematics
I, providing further exploration of numbers and arithmetic, geometry,
measurement, probability, and statistics from the point of view of prospective
early childhood and elementary school teachers. As in 43.110, problem solving
and the communication of mathematical ideas, both verbally and algebraically,
are strands that unite the course. Prerequisite: 43.110 College Mathematics
I or 43.113 Introduction to College Mathematics.
43.123 College Algebra (Gen.Ed. Goal 2)
Designed to provide the algebraic skills
needed in the natural sciences, social sciences, and precalculus. The course
emphasizes problem-solving skills, modeling and real-world applications, and
explores multiple approaches (numerical, graphical, and symbolic) to algebraic
concepts and problems. Topics include the real number system, algebraic
expressions, functions and graphs, polynomial and exponential functions,
matrices and systems of equations, and complex numbers. Note: A student may not
receive credit for both 43.123 and 43.115 College Algebra and Trigonometry.
Prerequisite: 43.095 General Mathematics or a satisfactory score on the
mathematics placement examination.
43.200 Precalculus (Gen.Ed. Goal 2)
A thorough introduction to the basic
mathematical functions used in the sciences and the background needed to study
calculus. After a brief in-depth review of the required algebra and analytical
geometry, topics include functions and graphs, polynomial and rational
functions, exponential and logarithmic functions, and trigonometric functions.
Note: A student may not receive credit for 43.200 Precalculus and 43.133
Precalculus, or for 43.200 Precalculus and 43.115 College Algebra and
Trigonometry. Prerequisite: 43.123 College Algebra or a satisfactory score
on the mathematics placement examination.
43.201 Intuitive Geometry
An introduction to the fundamental ideas of
geometry for prospective teachers. Geometric objects and relationships are
studied through intuitive, coordinate, vector and synthetic approaches. The
course builds from an informal approach, stressing visualization in two and
three dimensions, to the development of mathematical reasoning.
Prerequisite: One credit-bearing course in college mathematics or permission
of the instructor.
43.208 Biostatistics
A course that covers statistical methods as
they apply to the biological, health, and food sciences. The major emphasis is
on hypothesis testing, including regression and analysis of variance.
Descriptive statistics is also included. The statistical package Minitab is
used. Note: A student may not receive credit for both 43.208 Biostatistics and
43.117 Introduction to Statistics or 23.304 Biometrics. Prerequisite: One
credit-bearing course in college mathematics.
43.215 Finite Mathematics
A study of mathematical models in various
disciplines. Topics include logic, sets, functions, combinatorics, probability,
matrices, Markov chains, linear programming, game theory, and digraphs.
Prerequisite: 43.123 College Algebra or a satisfactory score on the
mathematics placement examination.
43.219 Calculus I (Gen.Ed. Goal 2)
A study of functions, limits, continuity, the
derivative, rules of differentia-tion of algebraic and trigonometric functions,
applications of differentiation, definite and indefinite integrals, the
Fundamental Theorem of Calculus, and applications of
integration. Prerequisite: 43.200 Precalculus or a satisfactory score on the
mathematics placement examination.
43.220 Calculus II
A study of the applications of the integration,
logarithmic and exponential functions, elementary differential equations (first
order linear and separable variables), techniques of integration, improper
integrals, L'Hospital's Rule, sequences, series, Taylor and Maclaurin Series,
application of series. Prerequisite: 43.219 Calculus I.
43.221 Calculus III
A study of conic sections; vectors in two and
three dimensions; dot and cross products and their applications to geometry;
equations of lines and planes; quadratic surfaces; polar, cylindrical, and
spherical coordinates; and functions of several variables, partial derivatives,
differentials, directional derivatives, gradients, optimization problems,
multiple integrals and their applications. Prerequisite: 43.220 Calculus
II.
43.222 Differential Equations
Topics in differential equations with special
emphasis on applications in the sciences. Topics covered include equations of
the variable separable type, exact, homogeneous and Bernoulli equations, the
method of substitution, approximation methods, linear equations, series
techniques, Laplace transforms, systems of equations, and the Sturm-Liouville
theory. Prerequisite: 43.221 Calculus III and 43.226 Linear Algebra and
Applications.
43.226 Linear Algebra and Applications
Vector spaces, subspaces, linear dependence,
bases, dimension, linear mappings, linear equations, matrices, inner products
and norms, determinants, quadratic forms, and the spectral theorem. Applications
of the above topics are given to various fields outside of mathematics.
Prerequisite: 43.219 Calculus I.
43.292 Discrete Mathematics I
A mathematical foundation for computer
science. Topics include logic, boolean algebra, sets, functions, sequences, and
summations, matrices, mathematical induction, study of algorithms, recursion,
combinatorics, graphs, and trees. Note: A student may not receive credit for
both 43.292 Discrete Mathematics I and 43.320 Discrete Mathematics.
Prerequisite: 43.200 Precalculus and 63.252 Computer Science II with
Advanced C, or permission of the instructor.
43.294 Discrete Mathematics II
A study of discrete mathematical structures.
Topics include a brief review of sets and an exploration of relations, graphs,
trees, digraphs, finite-state machines, formal languages, boolean algebra, and
combinatorial circuits. Prerequisite: 43.292 Discrete Mathematics
I.
43.301 Problem Solving and Modeling in Mathematics
A study in problem solving with the
development of banks of problems appropriate to various grade levels and
selected from arithmetic, informal geometry, logic, measurement, number
sequences, probability, and statistics, challenging enough to provoke interest,
but realistic enough for successful experiences. Heuristics, problem solving
techniques, Polya's stages of problem solving, specific strategies, and
pedagogical issues are studied. Prerequisite: 43.201 Intuitive Geometry and
43.215 Finite Mathematics.
43.307 Intermediate Statistics
A study of regression and correlation
analysis, chi square tests and contingency tables, design of experiments,
analysis of variance, non-parametric statistics, and introduction to data
analysis. Prerequisite: 43.117 Introduction to Statistics.
43.308 Applied Statistical Data Processing
Practical aspects of data analysis using
statistical computer packages such as MINITAB, SPSSX, AND BMDP. Multivariate
statistical methods including multiple regression, analysis of covariance,
factor analysis, multidimensional scaling, discriminant analysis and linear
models for cross-classified categorical data are emphasized. Students do
individual data analysis projects. Prerequisite: 43.307 Intermediate
Statistics.
43.310 Number Theory
A study of properties of numbers. Topics
include mathematical induction, divisibility, primes, congruences, the Chinese
remainder theorem, primitive roots, quadratic reciprocity, continued fractions,
partitions, and history of classical problems. Prerequisite: 43.220 Calculus
II.
43.313 Numerical Methods
A study of topics from elementary numerical
analysis: finite differences, solution of equations, interpolation, numerical
integration, and numerical linear algebra. Computer exercises and applications.
This course is recommended as preparation for the numerical analysis half of the
Part 3 Actuarial Exam. Prerequisite: 43.220 Calculus II and 63.152 Computer
Science I Using C. Recommended: 43.226 Linear Algebra and
Applications.
43.317 Introduction to Higher Geometry
A precise, rigorous examination of the axioms
and content of Euclidean geometry. In addition, non-Euclidean geometries are
discussed. Fields are discussed, and ruler-compass constructions are studied via
the device of quadratic extension fields. Prerequisite: 43.219 Calculus
I.
43.319 Modern Algebra
A study of algebraic structures and related
concepts including sets, logic, mappings, the integers, the division algorithm,
groups, rings, integral domains, fields, and polynomials. Note: A student may
not receive credit for both 43.319 Modern Algebra and 43.335 Algebraic
Structures I. Prerequisite: 43.226 Linear Algebra and
Applications
43.323 Advanced Calculus
Vector differential calculus, vector integral
calculus including the theorems of Green, Gauss and Stokes, maxima and minima
for functions of several variables, Language multipliers, uniform covergence of
sequences and series of functions, inverse and implicit function theorems, and
Jacobians. Prerequisite: 43.221 Calculus III, 43.226 Linear Algebra and
Applications.
43.324 Applied Mathematics
The study of problems arising from real-world
situations and the mathematical methods used in their solution. Topics include
mathematical modeling, continuous and discrete models, linear systems, Fourier
series, partial differential equations, and computer implementation of
solutions. Prerequisite: 43.222 Differential Equations, 63.152 Computer
Science I Using C, and a course in probability, statistics or finite
mathematics; or permission of the instructor.
43.331 Principles of Actuarial Mathematics
An introduction to mathematical applications
in the actuarial fields of theory of interest and survival analysis. Topics from
the theory of interest include simple and compound interest, annuities,
amortization schedules, and sinking funds. Topics from survival analysis include
death rates, standardized mortality ratios, common survival distributions, and
cohorts, current and select life tables. Prerequisite: Two semesters of
calculus, a statistics course, and, recommended, a computer science
course.
43.333 Operations Research and Modeling
A study of mathematical models of interest in
operations research. Topics selected from linear programming, transportation
problems, network analysis, nonlinear and dynamic programming, game theory,
probability models, queuing systems, inventory and simulation. Software packages
are used to solve real-life problems on the computer. Prerequisite: Two
semesters of calculus, one computer science course, one course in probability,
statistics or finite mathematics. Recommended: 43.226 Linear Algebra and
Applications.
43.348 Mathematical Statistics I
Sample spaces, events as subsets of a sample
space, probability axioms, combinatorics applied to probability problems, random
variables and their distributions, special distributions, multivariate
distributions, central limit theorem, and topics in statistical inference.
Prerequisite: 43.221 Calculus III plus either 43.215 Finite Mathematics or
43.226 Linear Algebra and Applications.
43.349 Mathematical Statistics II
Estimation, decision theory and hypotheses
testing, linear models, regression, analysis of variance, analysis of
categorical data, and nonparametric inference. Prerequisite: 43.348
Mathematical Statistics I.
43.404 Seminar
An exploration of an advanced topic in
mathematics or computer science. The particular topic is announced at least one
semester in advance. Prerequisite: Permission of the
instructor.
43.420 Topology
Topology of the real line, Bolzano-Weierstrass
and Heine-Borel theorems, Cauchy sequences and completeness, Hausdorf spaces,
continuous functions, compactness and connectedness, metric and normed spaces,
complete metric spaces, and separation axioms.
43.427 Real Analysis
Set theory, relations and functions,
properties of the real number system, topology of the real line, introduction to
metric spaces, limits of sequences and functions, continuous functions,
differentiation, and the Riemann-Stieltjes integral. Prerequisite: 43.221
Calculus III.
43.490 Directed Study
Student research on a topic or topics in
higher mathematics or computer science. Suggested areas include applied algebra,
numerical analysis, and mathematical physics. The student should make
arrangements with the faculty member who is to direct the work one semester in
advance of the work.
43.496 Internship in Mathematics
The student is encouraged (and assisted to
whatever extent possible) by the Mathematics Department to seek employment
during summers or part time during the school year, involving non-trivial
applications of mathematics. In this manner the student can earn up to three (3)
course credits, the amount of credit being decided by the student's advisor and
the department chair. Prerequisite: Approval of the chair
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