Department Chair

  • Edwin Rogers, Ph.D.
    Professor of Mathematics
    Roger Bacon Hall 444
    (518) 783-2392
    rogers@siena.edu

Courses

MATH 010 - Finite Mathematics
Much of the mathematics which impinges on everyday life is of the finite variety. This course will introduce students to topics from Number Theory, Combinatorics, Complexity Theory, Difference Equations, Game Theory, Geometry, Graph Theory, Information Theory, Group Theory, Logic, Probability and Simple Descriptive Statistics, and Set Theory. Prefer- ence will be given to topics which convey to the student the prevalence of finite mathematics in modern society, with applications which are accessible to student experimentation Primarily intended for Liberal Arts and Business majors. (ATTR: ARTS, CAQ)

MATH 030 - History of Mathematics
This is a one semester course on selected topics in the history of methematical ideas. Topics covered may include the notions of limit, infinity, area, parallelism, pi, transcendental numbers, number systems, mensuration, polynomials, cosmology, map coloring, logic, proof, abstraction, generalization, quadrature, trisection, or algebraic structure. The history of a given idea will be traced, and relevant problems will be presented. This course is intended for students in all schools of the College. Mathematics majors may take this class for elective credit but it does not count towards the requirements for the major. Offered spring semester. (ATTR: ARTS, CAQ)

MATH 050 - Preparation for Calculus
A study of the background material needed for calculus with emphasis on functions. The course includes a study of relations, functions and graphs, polynomials, solving equations and inequalities, rational and radical functions, logarithmic and exponential functions, trigonometric functions both right angle and analytic, vectors, polar and parametric equations, and an introduction to the conic sections. Students must purchase an approved graphing calculator prior to beginning this course. (ATTR: ARTS)

MATH 110 - Calculus I
Courses MATH- 110, 120, and 210 provide foundation for all upper level mathematics courses. Main topics considered during the first semester: functions, limits, continuity, differentiation, the chain-rule, antiderivatives, the definite integral, Fundamental Theorem of Calculus and trigonometric functions. Applications of all topics are emphasized. Three hours of lecture and one hour and twenty minutes of laboratory per week. Lab fee. Students must purchase an approved graphing calculator prior to begining this course. (ATTR: ARTS, CAQ)

MATH 120 - Calculus II
This course completes the calculus of elementary transcendental functions. It also includes techniques of integration, indeterminate forms, L'Hospital's Rule, improper integrals, and introduction to sequences, infinite series and power series. Students apply concepts to work, volume, arc length, and other physical phenomena. Three hours of lecture and one hour and twenty minutes of laboratory each week. Lab fee. Students must purchase an approved graphing calculator prior to beginning this course. (Effective Spring Semester 1994.) (ATTR: ARTS CAQ)

MATH 191 - Mathematical Problem Solving
An introduction to the art and craft of mathematical problem solving. Students interact in a seminar setting, discussing and solving interesting mathematical problems. Oral presentations of problems and solutions are a required part of this course. There are no prerequisites. (ATTR:ARTS)

MATH 210 - Calculus III
This course completes the Calculus sequence. The topics covered are vectors in the plane and in a three dimensional space, functions of several variables, partial differentiation, the chain rules, multiple integration including cylindrical and spherical coordinate systems and the theorems of Green and Stokes. Students apply these concepts to physical applications. (ATTR: ARTS)

MATH 230 - Linear Algebra
This course studies elements of linear algebra with an emphasis on applications. Topics covered include matrices, systems of equations, finite dimensional vector spaces, linear transformations, eigenvalues and eigenvectors. (ATTR: ARTS)

MATH 250 - Discrete Structures I
This course includes a study of mathematical structures most frequently encountered in Computer Science. Topics covered include sets, functions, mathematical induction, complexity analysis of algorithms, counting methods including probability, recurrence relations, graphs, trees, Boolean logic, and relations. Proofs using mathematical induction will be emphasized. Other proof techniques will be developed. Three hours of lecture and 80 minutes of lab each week. Offered Fall Semester. Cross-listed as CSIS-251. (ATTR: ARTS)

MATH 301 - Foundations of Mathematics
The course introduces logic, set theory and techniques of mathematical proof. The main emphasis of the course is on composing logically correct mathematical arguments. Oral and written presentation of solutions and proofs are a required part of the course, (ATTR: ARTS, MHUL)

MATH 310 - Intro to Modern Algebra
This course is an introduction to the elementary theory of groups and rings, developed axiomatically. Other topics covered are subgroups and closets, normal subgroups, factor groups, homomorphism and isomorphism of groups and rings, fundamental theorems for groups and rings. Offered Fall Semester. (ATTR: ARTS, MHUL)

MATH 320 - Mathematical Analysis
Introduction to the fundamental concepts of mathematical analysis. A two-term course that studies the real number systems, limits, sequences, series, convergence, uniform convergence, functions of one variable, continuity differ- entiability, Riemann integration, functions of several variables, line, surface, and volume integrals, Offered Spring Semester. (ATTR: ARTS, MHUL)

MATH 325 - Differential Equations
A study of differential equations using analytic, numerical and graphical techniques. Emphasis is placed on the formula- tion of models that result in a differential equation and the interpretation of solutions. Slope fields, graphs of solutions (analytic and numerical), vector fields and solution curves in the phase plane will be used to gain a better understanding of differential equations. Computer based tools will be used to investigate the behavior of solutions both numerically and graphically. Offered Spring Semester. ATTR: ARTS, MHUL

MATH 330 - Intro to Applied Mathematics I
In this course there will be applications of first and second order differential equations and linear algebra. The series solutions of the differential equations of Bessel and Legendre are studied in detail. Other topics include Fourier series and expansions as well as other series comprised of orthogonal functions. Applications of these expansions will be discussed as time allows. (ATTR: ARTS, MUHL)

MATH 340 - Introduction to Number Theory
A discussion of the basic properties of the set of integers. Prime numbers and the Euclidean Algorithm. Number- theoretic functions, especially the Euler phi-function. Linear congruences and their applications to the solution of Diophantine Equations. Exponents and primitive roots. Quad- ratic residues and the Law of Quadratic Reciprocity. Offered in Spring Semester. (ATTR: ARTS, MHUL)

MATH 350 - Discrete Structures II
This course is a continuation of the study of mathematical structures most frequently encountered in Computer Science. Topics covered include deterministic and non-deterministic finite automata, regular, context-free and other languages, push-down automata, grammars, Turing machines, computational complexity, and in particular the P vs. NP problem. Offered in Spring Semester. Cross-listed as CSIS-351. (ATTR: ARTS, MHUL)

MATH 360 - Euclidean Non-Euclid Geometry
An introduction to the techniques of Euclidean and Non- Euclidean geometry. Topics include: plane Euclidean geometry, geometric transformation groups, spherical geometry, the projective and hyperbolic planes. Offered Fall Semester. (ATTR: ARTS, MHUL)

MATH 371 - Probability for Statistics
The course introduces mathematical probability to understand variation and variability. Methods of enumeration, con- ditional probability, independent events, and Bayes' Theorem are developed in a general environment. Among the continuous and discrete probability distributions derived and studied are the Bernoulli distribution and distributions based on it, the uniform, exponential, normal, Gamma and Chi Square distributions. The Central Limit Theorem leads to approximations for discrete distributions. Chebyshev's In- equality prepares the student for Inferential Statistics. (may be taken concurrently). Offered Spring semester. (ATTR: ARTS, MHUL)

MATH 425 - Differential Geometry
This course is an introduction to the theory of curves and surfaces in the three-dimensional Euclidean space. Topics include curve arc length, curvature, torsion, the Frenet n-frame, the first and second fundamental forms of a surface, normal and principal curvatures, Gaussian and the mean curvatures, isometries of surfaces, and geodesic curves on a surface. (ATTR: ARTS, MHUL)

MATH 430 - Intro to Applied Math II
Applications of Fourier series and expansions to the solution of the classical partial differential equations of mathematical physics and an introduction to complex variables. (ATTR: ARTS, MHUL)

MATH 440 - Complex Variables

An introduction to the study of functions of a complex variable. Topics will include complex numbers, sequences, analytic functions, Cauchy-Riemann equations, complex integration, Laurent and Taylor Series, residue theorem, and conformal mapping. Offered in Fall Semester. (ATTR: ARTS, MHUL)

MATH 460 - Topology
This is a one semester introductory course in Topology. The topics covered include: Open and closed sets, topologies on general point sets, connectedness, compactness, continuity, product and quotient topologies, and metric spaces. Applica- tions to other areas in mathematics (principally geometry and analysis) will be explored. Offered Spring Semester. (ATTR: ARTS,MHUL)

MATH 470 - Mathematical Statistics
Statistical tests for multivariable problems are developed and applied to real data sets. The computer and the SPSS package will be used. Offered Fall Semester. (ATTR: ARTS, MHUL)

MATH 480 - Mathematics of Finance
This course builds on the knowledge base contained in previous courses taken by actuarial students. The goal is to reinforce understanding of the fundamental concepts of financial mathematics, and how those concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for future use. Students will review basic financial instruments and expand their knowledge base to more modern financial analysis using yield curves, spot rates and immunization. Finally, students will be introduced to the concept of risk management and understand how principles such as derivatives, forwards, futures, short and long positions, call and put options, spreads, collars, hedging, arbitrage, and swaps affect a firms' risk. Pre-requisite Finc 301, Finc 315 and Math 120, or permission of instructor. (ATTR: ARTS, BUS, MHUL)

MATH 490 - Mathematics Seminar
Consideration of a mathematical topic selected on the basis of faculty and student interest. Designed for students with good mathematical backgrounds. May be taken twice with different topic. Permission of instructor or department required for registration. Offered Spring Semester. (ATTR: ARTS, MHUL)

MATH 499 - Independent Study in Math
Study or research on an advanced mathematics topic under the tutelage of a qualified faculty member. May be taken more than one semester. Permission of faculty mentor and department head required for registration. (ATTR: ARTS, MHUL)