MAJOR IN MATHEMATICS (36 credits)
MTH 236 Calculus IV, together with prerequisites Calculus I, II, & III or the equivalent of any or all of these (e.g., high school AP)
MTH 244 Linear Algebra
MTH 441 Historical Perspectives in Mathematics (the Jr/Sr capstone course)
(prerequisite: Jr/Sr standing plus consent of the instructor)
Choose one course (3 credits) from:
MTH 333 Geometry MTH 431 Modern Algebra I
MTH 437 Theory of Numbers MTH 445 Real Analysis
Choose one course (3 credits) from:
MTH 336 Differential Equations (prerequisite: MTH 126)
MTH 341 Probability (prerequisite: MTH 125)
MTH 342 Statistics
MTH 439 Numerical Analysis (prerequisite: MTH 126)
Choose the remaining credits from courses in Mathematics numbered
111 or higher.
GROUP MAJOR IN MATHEMATICS-COMPUTER SCIENCE (54 credits)
REQUIRED: 11 courses (33 credits)
CMP 111 Computer Science I CMP 439 Numerical Analysis
CMP 112 Computer Science II MTH 122 Discrete Math
CMP 221 Data Structures MTH 125, 126, 235 Calculus I, II, III
CMP 222 Computer Architecture MTH 244 Linear Algebra
CMP 344 Design & Analysis
Choose 21 credits from computer science or mathematics which count
toward a major that consists of at least 6 credits from computer science
and 9 credits from mathematics.
NOTE: Credit toward the
major/minor or group major involving mathematics is given only for
courses numbered 111 and above.
MINOR IN MATHEMATICS (18 credits)
MTH 236 Calculus IV, together with the prerequisites Calculus I, II, III or the 15 credits from Mathematics courses numbered 111 or higher.
TEACHER EDUCATION REQUIREMENTS:
Teaching major in Mathematics: MTH 125, 126, 231, 233, 235. Elect 3 credits from MTH 232, 244. Elect 3 credits from MTH 241, 242. Elect 6 credits from MTH 236, 237, 239, 345 or any computer science course and the major in Mathematics.
Teaching minor in Mathematics: MTH 125, 126, 231, 233, 235. Elect 3 credits from MTH 241, 242; elect 3 credits from any Mathematics course numbered 111 or above.
Mathematics majors who wish to be recommended to the Teacher Education Committee for admission to the Teacher Education Program and for student teaching must have at least a 2.50 GPA in the Mathematics major. Other students who wish to be recommended for a teaching minor in Mathematics must have at least a 2.50 GPA in the Mathematics minor.
A. SERVICE COURSES: MTH 017, 019, 093, are for students who need preliminary preparation for further math related studies.
B. INTRODUCTORY COURSES: The courses, Mathematics as a Human Pursuit, and Discrete Mathematics, Math 111 and 121, provide appropriate background for doing or appreciating mathematics and computer science at a level beyond that done in high school. Calculus I and II, Math 125 and 126, provide experience working with change, limits, certain algorithms, and theorems basic to their application.
C. INTERMEDIATE COURSES:
Real Analysis, MTH
445, is the culmination of the analysis segment of the mathematics
program at Saint Joseph's College. The student should become
comfortable in doing theoretical thinking and proving in the calculus
and the set of real numbers, including its metric.
Linear Algebra, MTH 244, prepares the student to work with systems of linear equations, in matrix form for the most part, and to consider the properties of vector spaces.
Calculus III, Differential Equations, Numerical Analysis, MTH 235, 336, and 439 extend the work done in the introductory calculus sequence. Students experience the quantitative infinite and infinitesimal in both the discrete and continuous case, series and directional derivatives. Most equations cannot be solved by traditional, symbolic means; the student experiences the use of modern technology to find solutions with numerical methods.
Probability, Statistics, MTH 341 and 342, consider the fundamental concepts of probability theory and inferential statistics. The emphasis is on gaining skills working with applications of these concepts. The student is required to use computer packages, such as Derive,TrueBASICProbability, and SPSS as a regular part of these courses.
Geometry, MTH 333, provides a critical examination of the foundations of plane geometry, using an axiomatic approach. It includes the study of both Euclidean and non-Euclidean geometries. Proofs are emphasized.
Modern Algebra I, II and Theory of Numbers are intended to provide experience in proving concepts from given hypotheses.
Modern Algebra I & II, MTH 431 and 432 study groups, rings, and field theory, with the subsystems of these algebra's.
Theory of Numbers, MTH 437 considers properties of the integers. The student should become proficient in the use of mathematical induction.
D. ADVANCED COURSES
Historical Perspectives of Mathematics, MTH 441, is the capstone of the mathematics program. It is a seminar on historical topics from the great theorems and thinkers of mathematics. Students make oral and written presentations from their independent, though not necessarily original, research. Portfolios are to be kept by each student, in addition to the ones kept by the math department chair.
Topics in Mathematics, MTH 446, allows students with
demonstrated skills and background to select, with a designated
professor, topics to be studied during a semester. Topics might be
chosen from such subjects as Vector Analysis, Complex Variables,
Cryptology, Fractals, Chaos Theory, or even Actuarial Studies including
the SAS statistical computer package.
In every course numbered 125 and higher, the professor completes an assessment sheet for each student. These assessments do not supplant the grade for the course. These sheets are routinely placed in the student's folder (portfolio) kept in the office of the department chair. They are available to be seen by the individual student at their request. The faculty of the math department use them regularly as instruments for assessing the student's progress and as an internal evaluation of the mathematics program at Saint Joseph's College.
MTH 017. Basic Algebraic Skills 3 credits
This course is intended as either a refresher course or a first course in algebra for those students who have been away from mathematics studies for some time. The course treats the following topics: operations on real numbers, linear equations and inequalities, exponents and polynomials, rational expressions, roots and radicals, and quadratic equations. The assignments will include attacking "word problems" as part of the skills to be acquired.
MTH 093. Pre-Calculus 3
This course is intended for those who wish to study the Calculus, but need some preliminary mathematical work. It begins with some fundamentals of algebra, including sets, functions, and graphs. It treats of polynomial and rational functions, and includes the usual transcendental functions. It considers trigonometric identities and certain elements of analytic geometry, including conic sections. Some study of combinatorics is pursued.
MTH 111. Mathematics As a Human Pursuit 3
It is widely accepted that mathematics is necessary for modern technology; mathematics also makes a basic contribution to other aspects of human life. This course is designed to integrate the student's knowledge and study of mathematics with other experiences and disciplines. It pursues a problem solving approach to some consumer issues, the arts, elements of probability, voting, some number theory, and geometry. At least one segment of the course will treat contemporary concerns found in the news media which are based on statistical concerns.
MTH 122. Discrete Mathematics 3 credits
This is an introduction to logical and algebraic structures and combinatorial mathematics. Topics include methods of proof, recursion, Boolean algebra, recurrence relations, graph theory, finite automata, theory of computation with examples of applications to the field of computer science.
MTH 125. Calculus
Including a review of pre-calculus, this course is an introduction to the calculus through concepts involving limits of functions, continuity at a point, and the derivative. Differentiation of products, quotients, and composite functions are treated. Implicit differentiation, the Extreme Value Theorem and the Mean Value Theorem are also considered. Graph sketching noting asymptotic behavior, extrema, concavity, and related concepts complete the content. The course will include a laboratory session with the computer algebra system Maple and will incorporate the use of a scientific graphics calculator as a regular part of the study. Each student is expected to have either the suggested calculator or one approved by the instructor.
MTH 126. Calculus
II 3 credits
Continuing the introduction to the calculus, the theory and techniques of integration are introduced with analytic geometry, then Riemann sums, and then the Fundamental Theorem of Calculus. Applications of the definite integral include area of regions, volumes, arc length and surface area. The laboratory section will continue the use of the Computer Algebra System and the graphics calculator will again be used on a regular basis. Prerequisite: MTH 125 or department approval.
MTH 235. Calculus III 3 credits
This course continues the calculus sequence. A main thrust is its opening in-depth study of infinite sequences and series, including power series, Taylor series and Taylor polynomials. Conic sections, parametric equations and polar coordinates -- together with whatever review is required -- are studied as they relate to calculus concepts. Vector theory and the geometry of space are also treated. Prerequisite: MTH 126 or department approval.
Calculus IV 3 credits
This concluding portion of the calculus sequence begins with a brief review of vectors followed by a pursuit of vector-valued functions. Functions of several variables, with their attendant partial derivatives, extrema, and multiple integration with applications are studied. The directional derivative, tangent planes and normal lines follow from the vector considerations. Prerequisite: MTH 235 or department approval.
MTH 244. Linear Algebra 3 credits
This course studies linear transformations and linear algebras, including the study of solutions to systems of linear equations. It treats the theory of matrices leading to the theory of vector spaces over a field. It studies the operations on matrices, including determinants, and uses these concepts in a variety of applications. Prerequisite: MTH 125 or consent of the instructor.
Differential Equations 3 credits
This course studies differential equations from a practical viewpoint. It combines the formal exercises of integrating the various standard types of differential equations with the setting-up of equations for problems from the natural sciences. Prerequisite: MTH 126 or equivalent.
Probability 3 credits
This course is an introduction to probabilistic models and the theory of probability. It includes the study of conditional probability, random variables of one, two and higher dimensions, as well as some characterizations of discrete and continuous random variables. Prerequisite: MTH 125 or consent of the instructor.
Statistics 3 credits
This course presents an introduction to inferential statistics beginning with a brief overview of descriptive statistics and probability, including discrete and continuous distributions, and the central limit theorem. The main emphasis is on estimation, hypothesis testing, and selected tests for small samples. It culminates in analyses of variance and bivariate data with correlation and linear regression. Prerequisite: MTH 125 or consent of the instructor.
MTH 355. Independent Study 1-3 credits
MTH 390. Internship 3-9 credits
MTH 431. Modern Algebra I
This course is that portion of Abstract Algebra which studies elementary group theory. It considers the properties of groups, subgroups, and functions; this leads to groups of permutations and groups isomorphic to them. Homomorphisms of groups along with the induced quotient groups culminate in the Fundamental Homomorphism Theorem; this rounds out the course.
MTH 432. Modern Algebra II
This course is that portion of Abstract Algebra which studies elementary ring theory including ideals and quotient rings. It follows with a study of field theory and closes with a look at rings of polynomials and extension fields. Prerequisite: MTH 431 or consent of instructor.
437. Theory of Numbers 3 credits
This course treats the elementary properties of integers. It studies divisibility of integers, Euclid's Algorithm, solutions to Diophantine Equations, prime numbers, congruencies and quadratic residues.
MTH 441. Historical Perspectives in
This course, the capstone, is a seminar on historical topics from the great theorems and thinkers of mathematics. Students make oral and written presentations from their independent, though not necessarily original, research. Portfolios are to be kept by each student. Prerequisite: Junior or Senior Math major or consent of the instructor.
MTH 445. Real Analysis 3 credits
This course is a modern, topological approach to real analysis. It deals with the concepts of bounded sets; convergence of sequences and sub-sequences of real numbers; continuous functions on metric spaces; open and closed sets; connectedness, completeness, and compactness; Riemann integrals and derivatives; law of the mean; fundamental theorems of calculus; and improper integrals. Prerequisite: MTH 235 or consent of the instructor.
MTH 446. Topics in Mathematics 3 credits
Students with demonstrated skills and background may select, with a designated professor, topics to be studied during a semester. Topics might be chosen from such subjects as vector analysis, complex variables, cryptology, fractals, chaos theory, or even actuarial studies, including the SPSS statistical computer package. Prerequisite: consent of the instructor.
|Course Syllabi||Web Sites|
|MTH 111 Mathematics as a Human Pursuit||Web Site for M111|
|MTH 122 Discrete Mathematics||Web Site for M122|
|MTH 125 Calculus I|
|MTH 126 Calculus II|
|MTH 231 Modern Algebra I||
|MTH 232 Modern Algebra II|
|MTH 233 Geometry|
|MTH 235 Calculus III||
|MTH 236 Calculus IV
||Web Site for MTH 236
|MTH 336 Differential Equations||
|MTH 237 Theory of Numbers|
|MTH 439 Numerical Analysis||Web Site for MTH439
|MTH 241 Probability||
|MTH 242 Statistics|
|MTH 244 Linear Algebra||
|MTH 441 Historical Perspectives in Mathematics||
|MTH 445 Real Analysis||
|MTH 446 Topics in Mathematics||