Professors:
Walter
Czarnec, Thomas Koshy, Mohammond Salmassi, Sonja Sandberg
Associate Professor: Sarah
Mabrouk,
Joyce Cutler
Assistant Professors:
Eileen Lee, Julie L. Levandosky, Robert Page, Jr., Victoria Sapko
The General Education
Requirement
All
students must satisfy a general education requirement consisting of
eleven (11) courses outside of the major department (see page 60). The
General Education Goal 2 (Quantitative) requirement is satisfied through
the completion of the Mathematics major.
Courses may have specified conditions for enrollment, such as prior
completion of less advanced courses, permission of the instructor,
or
appropriate placement test scores. Students should refer to course
descriptions in the department listings for prerequisite requirements.
Each
incoming student must take a placement examination in writing, which is
administered during orientation for new students. Shown below are
additional dates and times for the examinations during the 2006-2007
academic year. Contact the Center for Academic Support and Advising
(CASA) for reservations.
Tuesday,
September 1, 2006
................................................
9:30 am
Tuesday,
September 1, 2006
................................................
1:30 pm
Wednesday,
October 25, 2006
..............................................1:30
pm
Thursday,
October 26, 2006..................................................4:30
pm
Tuesday, January 23,
2007....................................................
4:30 pm
Wednesday, March 28,
2007..................................................1:30
pm
Thursday, March
29,
2007
....................................................4:30 pm
Mathematics Code Interpretation
0
May not take a credit-bearing math course at Framingham State College.
Student should first complete 43.095 General Mathematics or similar
course at another campus.
Q
Student may enroll in non-algebraic math courses: 43.110 College Math I
(for Coordinate majors in Education), 43.117 Introduction to Statistics,
and 43.119 Math for the Liberal Arts.
1
Student may take any 100-level math course listed above, as well as
43.123 College Algebra.
2
Student may enroll in any 100-level math course, plus 43.200 Precalculus
or, after consultation with the Mathematics Department, 43.219 Calculus
I.
All students must complete the following twelve (12) core courses:
43.215 Finite Mathematics
43.219 Calculus I
43.220 Calculus II
43.221 Calculus III
43.226
Linear Algebra and Applications
43.317
Introduction to Higher Geometry
43.319
Abstract 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.
CONCENTRATIONS IN MATHEMATICS
In
addition to the twelve (12) core requirements above, each student must
complete:
43.222 Differential Equations
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 and Technology: High
School/Middle School (Credit - two course credits)
14.410 Student Teaching Practicum and Seminar I-
Secondary (Credit-two course credits)
14.411 Student Teaching Practicum and Seminar II
-
Secondary (Credit-two coursecredits)
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 Abstract
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 the two
mathematics electives among the core courses.
A. Coordinate
Major in Early Childhood Education (Pre-K - Grade 2 Licensure)
14.200
Education in American Society with Field Study I
42.200
Psychology of Development
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 course credits)
14.432
Early Childhood Professional Practicum B (Credit—two course credits)
B. Coordinate Major in Elementary Education (Grades 1 - 6
Licensure)
14.200
Education in American Society with Field Study I
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 course credits)
14.438
Elementary Professional Practicum B (Credit—two course credits)
Note:
42.200
may be used to fulfill the college requirement for general education.
MINOR IN MATHEMATICS (5
COURSES)
43.219
Calculus I and four (4) courses at or above the 200-level. Students may
substitute
43.117
Introduction to Statistics for 43.200 Precalculus but only one of these
courses may receive credit towards the mathematics minor. These courses
are to be chosen under the guidance of a member of the Mathematics
Department.
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
1 Research
Methods in Psychology II
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).
MATHEMATICS COURSES APPROPRIATE FOR
GENERAL EDUCATION (GEN. ED.)
|
Courses |
|
Goal |
|
43.110 |
College Mathematics I |
2
|
|
43.117 |
Introduction to Statistics |
2
|
|
43.119 |
Mathematics for the Liberal Arts |
2
|
|
43.123 |
College Algebra |
2
|
|
43.200 |
Precalculus |
2
|
|
43.219 |
Calculus I |
2
|
COURSE DESCRIPTIONS
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 collegelevel 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 for the
Liberal Arts (Gen. Ed. Goal 2)
A survey of the beauty
and effectiveness of mathematics in describing natural and social
phenomena. Topics may include pattern recognition, logic, sets, number
systems, counting methods, probability, statistics, symmetry, population
growth, voting systems, or consumer mathematics. This course is
recommended for students whose major does not require 43.110 College
Mathematics I, or
43.117
Introduction to Statistics, or 43.123
College Algebra.
Prerequisite: Satisfactory score on the mathematics
placement exam.
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 indepth
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
A study of the methods
for solving linear and elementary nonlinear 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; approxima
tion
methods; linear equations; series techniques;
Laplace transforms; systems of equations; and the
Sturm-Liouville theory.
Prerequisites: 43.220 Calculus II and 43.226
Linear Algebra and Applications.
43.226 Linear Algebra and
Applications
A study of vector spaces,
subspaces, linear dependence, bases, dimension, linear mappings, linear
equations, matrices, inner products and norms, determinants, quadratic
forms, and the spectral theorem. Applications to various fields outside
of mathematics are examined. Prerequisites: 43.215 Finite Mathematics
and
43.220 Calculus II.
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. Prerequisites: 43.200 Precalculus and 63.252
Computer Science II Using Java, 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 explo
ration 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 or
43.208 Biostatistics.
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 crossclassified 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 Java. Recommended:
43.226 Linear Algebra and
Applications.
43.317 Introduction to Higher
Geometry
A precise, rigorous
examination of the axioms and concepts of various geometries. Euclidean,
non-Euclidian, and transformational geometries are investigated.
Ruler-compass constructions are discussed. Prerequisites: 43.219
Calculus I
43.319 Abstract Algebra
A study of algebraic
structures and related concepts including groups, rings, integral
domains, fields, and polynomials. Note: A student may not receive credit
for both 43.319 Abstract Algebra and 43.335 Algebraic Structures I.
Prerequisite: 43.310 Number Theory
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 Java 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 test
ing,
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 nontrivial 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.
|
