The Graduate School
Salem State University, 352 Lafayette Street, Salem, MA 01970.
Current and future courses offered
at the Master's level in Mathematics

Note:  We also have courses for a Master of Arts in Teaching Middle School Mathematics degree.  To see these courses (none of which count towards a Master of Science in Mathematics or Master of Arts in Teaching Mathematics degree), please go to  http://catalog.salemstate.edu/preview_program.php?catoid=32&poid=3588&returnto=5459

Summer II 2017: (July 10 - Aug. 19, 2017)
MAT710 Foundations of Mathematics (3 Cr.)     MW  6:30-9:30 p.m.  SB306A     Sec. 21  (1094)      D. Weiner
Suggested topics are: propositional and predicate calculi, consistency and completeness of axiom systems, Godel’s theorem, axiomatic set theory, cardinal and ordinal numbers.

MAT807 Statistical Inference (3 Cr.)    Wed.  4:15-6:15 p.m.  SB308F         D. Weiner
Prerequisite: Mathematical Statistics
A continuation of MAT707. Suggested topics are multiple regression, analysis of variance, decision functions, Bayes solutions, and nonparametric methods.

Fall 2017: (Sept. 6 - Dec. 22, 2017)  (tentative)
PLEASE REGISTER ON OR BEFORE  August 18 for Fall 2017 courses!!   If you are told before August 18 that a class is full, please e-mail arosenthal@salemstate.edu to find out if we can either add another section or give you permission to be added to a "full" class.  You may register online at http://navigator.salemstate.edu beginning on March 6.   If this link doesn't work, please go to http://www.salemstate.edu and click on the "Sign In" link in the upper right.

MAT711 Real Analysis I (3 Cr.)    Tues.  4:30-6:50 p.m  SB301   Sec. S1  (1292)      Y. Levin
Prerequisite: 12 hours of Calculus or the equivalent
Completeness, limits, continuity, convergence of sequences and series, derivatives, the Riemann integral, and theorems of Taylor, Bolzano-Weierstrass, and Heine-Borel together with applications.

MAT723 Numerical Analysis (3 Cr.)     Wed.  4:30-6:50 p.m.  SB305A   Sec. S1  (1293)    A. Rosenthal
Prerequisite: Ordinary Differential Equations
Suggested topics are least-square polynomial approximation, numerical integration, rootfinding, numerical solution of differential equations, direct and iterative methods in matrix theory, analysis of numerical stability.

Spring 2018: (Jan. 16 - May 9, 2018)  (tentative)
MAT725 Fractal Geometry (3 Cr.)
       Tues.  7:00-9:20 p.m.   Sec. S1  (1340)    A. Rosenthal
Prerequisite: Acceptance into either the Master of Science in Mathematics, Master of Arts in Teaching Mathematics or the Master of Science in Geo-Information Science program or permission of the Mathematics Graduate Program Coordinator.
A study of the geometry of fractal sets, self-similarity and fractal dimension.  Suggested topics are:  Iteration using the computer, graphical analysis, the Julia and Mandelbrot sets, chaos and applications to image compression, to dynamical systems and to computing the limiting perimeter and area enclosed by fractal sets.

MAT731 Measure and Integration (3 Cr.)    Mon.  7:00-9:20 p.m.  SB311  Sec. S1 (1341)   D. Weiner
Prerequisite: Real Analysis I or the equivalent
Suggested topics are: metric spaces, topological spaces, abstract measure; outer measure, absolute continuity, measure spaces, measurable functions, Lebesgue-Stieltjes integration, product measure, Caratheodory outer measure, L-spaces, the Radon-Nikodym theorem.

MAT740 Computer Applications in Mathematics I (3 Cr.)   Wed.  7:00-9:20 p.m.   Sec. S1 (1342)    A. Rosenthal
A programming language such as MATLAB is introduced and used to illustrate computer methods in Calculus, Number Theory, Algebra, Statistics and Economics. Attention is paid to machine accuracy, error estimation and multiple-precision arithmetic. Assignments include the coding and running of programs in the Computer Laboratory. No previous computer experience required. 

Summer I 2018: (May 21 - June 30, 2018)  (tentative)
MAT701 Vector and Tensor Analysis (3 Cr.)     MW  6:30-9:30 p.m.       Sec. 01   (1020)    D. Weiner
Suggested topics are: Definition of vectors and transformation equations, general Cartesian co-ordinates; vector and scalar products, geometry of space curves; introduction to differential forms and tensors.

MAT702N Research on Teaching Methods in Mathematics I (3 Cr.)   Tues.  4:30-7:30 p.m. (hybrid) 
Sec. 01  (1019)  T. Beckett
Prerequisites: Completed course in statistics and completion of the Measurement and Evaluation standard
This course will allow the student to find and study models of accomplished researchers on the teaching of Mathematics at the secondary level. The course will examine necessary concepts in research validity; data gathering; instrumentation selection and construction; validation and reliability determinations; sampling techniques; and research designing. Further, the course will review the application of statistical models salient to designs utilized in conducting research which requires the testing of hypotheses that have been generated from problems in secondary school Mathematics. Open only to M.A.T. and M.Ed. candidates for degree credit.

MAT705 Modern Plane Geometry (3 Cr.)    TuTh  4:30-7:30 p.m.    Sec. 01   (1020)   J. Belock
Prerequisite: Two semesters of Calculus
Suggested topics are: axiomatic approach to plane geometry, parallel postulate, Euclidean and hyperbolic geometries; quadratic extensions and angle trisection; plane measure.

Summer II 2018: (July 9 - Aug. 18, 2018)  (tentative)
MAT706 Theory of Numbers (3 Cr.)    TuTh  6:30-9:30 p.m.     Sec. 21 (1022)   A. Rosenthal
Prerequisite: Permission of the Department Chairperson or Mathematics Graduate Coordinator
Suggested topics are: properties of divisibility, linear congruences; quadratic congruences; prime numbers, continued fractions; number-theoretic functions; primitive roots and quadratic residues.

MAT 747 Applied Statistical Inference (3 Cr.)
    MW  6:30-9:30 p.m.     Sec. 21  (1023)   D. Weiner
Prerequisite: Acceptance into either the Master of Science in Mathematics, Master of Arts in Teaching Mathematics or the Master of Science in Geo- Information Science program or permission of the Mathematics Graduate Program Coordinator.
A study of probability and statistical inference. Suggested topics are: Probability, discrete and continuous probability distributions, sampling distribution theory, confidence intervals, tests of statistical hypotheses, linear regression, and a nonparametric method: the Kolmogorov-Smirnov Goodness-of-Fit Test; applications to spatial statistics. The emphasis of the course is on applications and conceptual understanding, rather than on mathematical derivations.

Fall 2018: (Sept. 5 - Dec. 20, 2018)  (tentative) 
MAT704 Linear Algebra (3 Cr.)    Mon.  4:30-6:50 p.m     Sec. S1
Prerequisite: 6 hours of Calculus and 3 hours of linear algebra comparable to our MAT 304A
Topics include modules, linear dependence, matrix algebra, linear transformations, determinants, eigenvalues, linear systems, inner products, classical groups, diagonalization, symmetric matrices, function spaces, and differential operators.

MAT 708 Introduction to Cryptography (3 Cr.)   Wed.  4:30-6:50 p.m.  Sec. S1
Prerequisite: Mathematical maturity as demonstrated by any one of the following – at least 12 credits of undergraduate or graduate math courses, or a score of 700 or higher on the math SAT or GRE.
An introduction to cryptography – the study of methods of sending messages in disguised form, including some recent applications of number theory and group theory to public key cryptography. Topics include elementary number theory, finite fields, group theory, cryptosystems, and public key cryptography.

MAT713 Ordinary Differential Equations (3 Cr.)    Thurs.  7:00-9:20 p.m    Sec. S1
Prerequisites: 9 hours of Calculus
Suggested topics are solutions of linear differential equations and systems of equations. Bessel and Legendre functions, Laplace transforms, series solutions, Sturm-Liouville theory, stability theory and singular points.

Spring 2019: (Jan. 10 - May 6, 2019)  (tentative)
MAT709 Complex Variables (3 Cr.)
   Thurs.  4:30-6:50 p.m.     Sec. S1
Prerequisite: Real Analysis comparable to our MAT 411 or MAT 711
Complex numbers, analytic functions, derivatives and integrals of complex functions, Cauchy integral theorem and formula, Taylor and Laurent series, residues, maximum principles, conformal mapping, families of analytic functions and analytic continuation.

MAT734 Linear and Multilinear Algebra (3 Cr.)   Wed.  4:30-6:50 p.m   Sec. S1
Prerequisite: Linear Algebra comparable to our MAT 414 or MAT 704
Suggested topics are: canonical forms for matrices and linear transformations, quadratic forms, principal axis theorem, tensor products, exterior and symmetric algebras.

MAT813 Partial Differential Equations and Fourier Series (3 Cr.)     Tues.  4:30-6:50 p.m.    Sec. S1
Prerequisite: Ordinary Differential Equations
Suggested topics are: wave equations, elliptic and parabolic equations; Fourier series; Sturm-Liouville theory and general Fourier expansions; eigenvalue expansions and Bessel functions.
estimation and multiple-precision arithmetic. Assignments include the coding and running of programs in the Computer Laboratory. No previous computer experience required. 

Summer I 2019: (May 20 - June 29, 2019)  (tentative)
MAT702N Research on Teaching Methods in Mathematics I (3 Cr.)   Sec. 01
Prerequisites: Completed course in statistics and completion of the Measurement and Evaluation standard
This course will allow the student to find and study models of accomplished researchers on the teaching of Mathematics at the secondary level. The course will examine necessary concepts in research validity; data gathering; instrumentation selection and construction; validation and reliability determinations; sampling techniques; and research designing. Further, the course will review the application of statistical models salient to designs utilized in conducting research which requires the testing of hypotheses that have been generated from problems in secondary school Mathematics. Open only to M.A.T. and M.Ed. candidates for degree credit.

MAT707 Mathematical Statistics (3 Cr.)    MW  6:30-9:30 p.m.  Sec. 01   
Prerequisite: 12 hours of Calculus
A calculus-based study of probability and statistics. Topics include probability models, discrete and continuous random variables and their distributions, bivariate and multivariate distributions, sampling distributions, limit theorems, point and interval estimation, theory and applications of hypothesis testing, linear regression and correlation.

MAT750 History of Mathematics (3 Cr.)     Sec. 01
Prerequisite: 9 Hours of Calculus
A survey course designed to deepen the student’s knowledge of the vast literature of mathematics. Historically influential concepts will be examined for their effects on mathematics and the culture in which they evolved. Philosophical and psychological comparisons will be made between the mathematical and scientific developments in Ancient Greek times, in the Renaissance and Newtonian times, and in the 19th and 20th centuries.

Summer II 2019: (July 8 - Aug. 17, 2019)  (tentative)
MAT710 Foundations of Mathematics (3 Cr.)     MW  6:30-9:30 p.m.      Sec. 21 
Suggested topics are: propositional and predicate calculi, consistency and completeness of axiom systems, Godel’s theorem, axiomatic set theory, cardinal and ordinal numbers.

MAT807 Statistical Inference (3 Cr.)    TuTh  6:30-9:30 p.m.      Sec. 21
Prerequisite: Mathematical Statistics
A continuation of MAT707. Suggested topics are multiple regression, analysis of variance, decision functions, Bayes solutions, and nonparametric methods.

Please send suggestions for courses you would like to see offered in these or future semesters to arosenthal@salemstate.edu.

Back to Top;      Home page for Salem State University Mathematics Graduate Programs

Author information:  Professor A. Rosenthal, Math Dept.   To send me e-mail, click on arosenthal@salemstate.edu
Copyright © 2017, Salem State University, Salem, MA 01970-5353.  All rights reserved.

Revised: July 12, 2017

Next scheduled revision: 
August 25, 2017 (when the classes running in Fall 2017 will be definitely known))