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Chair: Walter Czarnec
Professors: Walter Czarnec, Thomas Koshy, Kenneth
Preskenis, Sonja Sandberg
Associate Professors: *Anita Goldner, Mohammad Salmassi
Assistant Professors: Michelle Capozzoli, Joyce Cutler, Eileen Lee, Sarah
Mabrouk
*Sabbatical: Spring 2003
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 2002-2003
academic year, to be given in the Center for Academic Support and Advising
(CASA).
| Tuesday, September 3, 2002 |
10:30am |
| Tuesday, September 3, 2002 |
4:30 pm
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| Tuesday, October 22, 2002 |
4:30 pm
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| Wednesday, October 23, 2002 |
1:30 pm
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| Monday, January 22, 2003
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4:30 pm
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| Wednesday, March 26, 2003
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1:30 pm
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| Thursday, March 27, 2003
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4:30 pm
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MATHEMATICS MAJOR
All students must complete the following seven (7) core courses:
43.215 Finite
Mathematics
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
Two (2) electives in mathematics, one at the
200 level or above, one 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 2 Licensure)
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 Licensure)
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
43.335 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.
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
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: 43.200 Precalculus or permission of the instructor.
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 concepts of various geometrics. Euclidean, non-Euclidean, and transformational geometries are investigated. Ruler-compass constructions are discussed.
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.
43.348 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.
43.427 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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