## Department of Mathematics and Statistics

Distinguished Teaching ProfessorEdward S. Thomas Jr., Ph.D.

University of California, RiversideLouis Brickman, Ph.D.

University of PennsylvaniaVincent Cowling, Ph.D.

Rice UniversityHugh Gordon, Ph.D.

Columbia UniversityJoe W. Jenkins, Ph.D.

University of IllinoisMelvin L. Katz, Ph.D.

University of California, BerkeleyViolet H. Larney, Ph.D.

University of WisconsinHajimu Ogawa, Ph.D.

University of California, BerkeleyLindsay N. Childs, Ph.D.

Cornell UniversityEdward D. Davis, Ph.D.

University of ChicagoNathaniel A. Friedman, Ph.D.

Brown UniversityRichard Z. Goldstein, Ph.D.

University of PennsylvaniaBenton N. Jamison, Ph.D.

University of California, BerkeleyBoris Korenblum, Sc.D.

Moscow State UniversityTimothy L. Lance, Ph.D.

Princeton UniversityThomas H. MacGregor, Ph.D.

University of PennsylvaniaGeorge E. Martin, Ph.D.

University of MichiganRichard C. O'Neil, Ph.D.

University of ChicagoR. Michael Range, Ph.D.

University of California, Los AngelesHoward H. Stratton, Ph.D.

University of California, RiversideEdward C. Turner, Ph.D.

University of California, Los AngelesDonald R. Wilken, Ph.D.

Tulane UniversityKehe Zhu, Ph.D.

State University of New York at Buffalo

Associate Professors Emeritae/iElton Butler, M.A.

Columbia UniversityRobert Luippold, M.A.

University of BuffaloErich Nussbaum, Ph.D.

University of VirginiaJohn T. Therrien, M.A.

University at AlbanyGuy D. Allaud, Ph.D.

University of WisconsinHerbert I. Brown, Ph.D.

Rutgers UniversityHara Charalambous, Ph.D.

University of Illinois, Urbana-ChampaignWilliam F. Hammond, Ph.D.

Johns Hopkins UniversityLloyd L. Lininger, Ph.D.

University of IowaRicardo Nirenberg, Ph.D.

New York UniversitySteven Plotnick, Ph.D.

University of MichiganCarlos C. Rodriguez, Ph.D.

Columbia UniversityMalcolm J. Sherman, Ph.D.

University of California, BerkeleyMark Steinberger, Ph.D.

University of ChicagoMichael I. Stessin, Ph.D.

Moscow State UniversityMartin Victor Hildebrand, Ph.D.

Harvard UniversityKarin B. Reinhold-Larsson, Ph.D.

Ohio State UniversityAnupam Srivastav, Ph.D.

University of Illinois, Urbana-Champaign

Adjuncts (estimated): 0

Teaching Assistants (estimated): 30## Careers

The objective of the department is to serve the needs of students aspiring to careers that require mathematical background: physical, biological, social, and management sciences; statistics, actuarial work, computer science, applied mathematics; secondary school teaching; graduate work; college and university teaching; and research in mathematics. In most cases, training beyond the bachelor's degree is desirable and can often be obtained after the graduate has secured employment. The department also welcomes students who wish to study mathematics as part of a traditional liberal arts education.

## Placement and Proficiency Credit

The University awards up to 8 credits and advanced placement in its sequences of calculus courses based on performance on the advanced placement calculus examinations administered by the College Board. Details concerning the decisions on credit and placement are available from the Admissions Office.

## Admission

Students may not declare a major in either mathematics or actuarial and mathematical science until they have completed at least one of A Mat 113, 119, or 214 with a grade ofA,B,C, orS. Transfer credits and grades may be used to satisfy the requirement.

## The Mathematics Major

Students majoring in mathematics elect either the general program or the teacher education program. Under either program, a student may choose to complete the requirements for either the B.A. or B.S. degree. Under any of the four program-degree combinations, a student may apply for admission to the honors program.Students considering a major in mathematics are encouraged to visit the department office (ES-110) for advice. Information is also available at the web site http://math.albany.edu.

## Degree Requirements for the Major in Mathematics

B.A.:A minimum of 36 credits from the Department of Mathematics and Statistics in courses numbered above 110, including A Mat 214, 220, and a 3-credit course numbered above 300 in each of these four areas: algebra, analysis, geometry/topology, and probability/statistics.

B.S.:A minimum of 36 credits from the Department of Mathematics and Statistics in courses numbered above 110, including A Mat 214, 220, and any two of the following four options: (1) A Mat 326 and 327, (2) either (a) both A Mat 314 and 315 or (b) any two of 312, 412, 413, or 414, (3) any two of A Mat 342, 441, or 442, (4) either (a) A Mat 368 and 369, (b) A Mat 367 and 464, or (c) A Mat 467 and 468. With departmental approval, other 400-level or 500-level courses may be substituted for the courses listed above. In addition, each student must complete: 6 credits in computer science from A Csi 101N, 201N, 203, 204, 205, 310; and a minor in atmospheric science, biology, business, chemistry, computer science, economics, electronics, geology, or physics.NOTE: The Statistics minor is

notopen to students with a major in mathematics.

General ProgramStudents, with suitable advisement, can design programs which will best meet their particular interests and career goals. Note, however, that those who plan to do graduate work in any mathematical field-pure or applied-should obtain as strong an undergraduate background as possible in the basic areas of mathematics: algebra, analysis, and geometry/topology. In particular, they should make every effort to include A Mat 413 and 414 (Advanced Calculus) in their programs.

To guide students in their planning, a number of options, some of a general nature and others to meet specific career objectives, are presented here.

Liberal Arts (B.A.)

Some professional careers and many jobs require a mathematical background characterized more by breadth than by concentration in any particular area of the mathematical sciences. The purpose of the B.A. program is to assure that the student acquires a broad view of mathematics and statistics. Each B.A. major is required to complete a 3-credit course numbered above 300 in each of these areas: algebra, analysis, geometry/topology, and probability/statistics. The following lists those courses which can be taken to fulfill that requirement:Algebra: A Mat 326, 326Z, 424

Analysis: A Mat 311, 312, 312Z, 314, 409, 412, 412Z

Geometry/Topology: A Mat 331, 331Z, 342, 342Z, 432, 432Z, 441, 442

Probability/Statistics: A Mat 367, 367Z, 465, 465Z

Students are urged to explore in greater depth, preferably at the 400 level. Since students will have different goals, it is impossible to provide useful sample programs. Students are encouraged to devise their own plans in consultation with their advisers. However, if a student is to graduate on time, the calculus sequence and linear algebra should be completed during the freshmen and sophomore years.

Graduate School Preparation

The department offers excellent opportunities for students who plan to go on to graduate work in mathematics and statistics as well as other areas such as computer science, the natural sciences, and the social and behavioral sciences.Students whose goal is to obtain a graduate degree in mathematics should include in their programs as many of the following core courses as possible in each of the designated areas:

Algebra: A Mat 326, 327, 424

Analysis: A Mat 413, 414

Geometry/Topology: A Mat 342

Those hoping to do graduate work should also consider entering the honors program.

Applied Mathematics

Although it is common to classify mathematics as either "pure" or "applied," the division is often arbitrary. Some extremely abstract mathematics in recent years has turned out to be useful in areas outside mathematics. Thus, those students who are preparing for a career in applied mathematics would be well- advised to acquire as strong a background as possible in the pure mathematical areas of analysis, algebra, and geometry/topology. On the other hand, students concentrating in pure mathematics should have some understanding of how to apply mathematical methods to other disciplines.Listed here are the mathematical subjects that are more commonly applied to problems in other fields along with the corresponding courses in which methodology or applications are treated.

Applied algebra: A Mat 326, 372

Applied analysis: A Mat 311, 314, 315, 409, 412, 416

Numerical Methods: A Mat 313, 401

Probability/Statistics: A Mat 367, 368, 369, 464, 465

Statistics

Statistics is a widely applied branch of mathematics and the demand for statisticians is high. Preparation for a career or for advanced study in statistics should include one of the following two combinations of courses: (1) probability (A Mat 367 or 367Z, 464) and statistics (A Mat 368 or 368Z, 369 or 369Z, 465 or 465Z), or (2) probability (A Mat 367 or 367Z, 464) and statistics (A Mat 467, 468). Sequence (2) is recommended as the more advanced and thorough treatment. A Mat 424 (advanced linear algebra) is highly recommended. Also useful are A Mat 401, 409, 413 or 413Z, and 414. Because computing is a close adjunct to statistics, students are strongly advised to include A Csi 201N, 205, and 310 as a minimal introduction.

## Teacher Education Program

Students interested in a career in secondary school teaching must apply for and be admitted to the Teacher Education Program, which is administered by the School of Education, before they can be officially enrolled in the teacher education program with a major in mathematics. The admission requirements and the certification requirements are described in this bulletin under the School of Education. Note that students in the teacher education program must complete both the education professional requirements described under the School of Education and those courses within the major and related fields that are listed under "Degree Requirements for the Major in Mathematics."

- In addition to the education professional requirements, specific course requirements for the mathematics teacher education program are: 6 credits in the same one of these sciences-atmospheric science, biology, chemistry, geology, physics; and in mathematics: A Mat 326 or 326Z, 327 or 327Z, 331, 367 or 367Z, 368 or 368Z, 342 or 342Z, and 452 or 452Z; in addition, either A Mat 363 or 363Z or 367 or 367Z (A Mat 312 or 312Z is recommended for those wishing to teach calculus).

- Typical schedule of mathematics courses:
Year Fall SpringFresh. 112 or 118 113 or 119 Soph. 214 & 220 312 & 331 Junior 326 & 367 327 & 3638 Senior 342 & 452 Student TeachingNote particularly that at least two courses should be taken each semester beginning in the sophomore year.

## Honors Program

The honors program is designed for the talented and committed student of mathematics. Successful completion of the program is excellent preparation for graduate work in mathematics.

Students entering the University with strong mathematical backgrounds should consider taking Honors Calculus, A Mat 118 and 119, in place of the standard Calculus, A Mat 112 and 113.

A student may be admitted formally to the honors program at any time after the sophomore year, and then will be formally advised by the Director of the Honors Program. However, any student who is interested in the program should see the Director of the Honors Program as early as possible for informal advisement.

To be admitted, the applicant must have an academic average in all University courses of at least 3.30, and an academic average in all mathematics courses of at least 3.40. Specific course requirements are: A Mat 413 or 413Z, 414, 424, and 9 additional credits from among A Mat 327 or 327Z, 416, 420, 425, 432 or 432Z, 441, 442, 464, 467, 468, 510A, 513A, 520A, 520B, 540A, 557A, 557B, and independent study (maximum of 3 credits).

To be recommended for graduation with honors, the candidate must write an acceptable honors thesis and also maintain an academic average of at least 3.30 in all University courses and at least 3.40 in all mathematics courses numbered 400 or above.

## The Actuarial Major

Mathematics has useful and interesting applications in the field of actuarial science. Within the major is a sequence of courses covering the materials of course exams that correspond to the exams given by the Society of Actuaries. The specific applicable courses are as follows:Course Exam 100: A Mat 112 or 118, 113 or 119, 214, 220, 204

Course Exam 110: A Mat 467, 468, 469

Course Exam 120: A Mat 465

Course Exam 130: A Mat 372, 374

Course Exam 135: A Mat 401. A small amount of material on linear systems can be obtained by self study.

Course Exam 140: A Mat 301

Year Fall SpringFresh. 112 or 118 113 or 119 Soph. 214 & 220 204 & 301 Junior 367 & 401 368 & 372 Senior 465 & 467 374 & 468 & 469

## Degree Requirements for the Major in Actuarial and Mathematical Sciences

B.S. Actuarial and Mathematical Sciences (combined Major and Minor): 61 credits as follows:42 credits in mathematics: A Mat 112 (or 118), 113 (or 119), 214, 220, 301, 367 (or 367Z), 368 (or 368Z), 372, 374, 401, 465, 467, and 468

7 credits: A Csi 201N and 203

3 credits: B Acc 211

9 credits: as advised, in courses from the School of Business or having prefix A Csi or A Eco.

## Combined B.A./M.A. and B.S./M.A. Programs

The combined B.A./M.A. and B.S./M.A. programs in mathematics provide an opportunity for students of recognized academic ability and educational maturity to fulfill integrated requirements of undergraduate and master's degree programs from the beginning of their junior year. A carefully designed program can permit a student to earn the B.A or B.S. and the M.A. degrees within nine semesters.

The combined programs require a minimum of 138 credits, of which at least 30 must be graduate credits. In qualifying for the B.A. or B.S., students must meet all University and college requirements, including the requirements of the undergraduate major described previously, the minimum 90- or 60-credit liberal arts and sciences requirement, general education requirements, and residence requirements. In qualifying for the M.A., students must meet all University and college requirements as outlined in the Graduate Bulletin, including completion of a minimum of 30 graduate credits and any other conditions such as a research seminar, thesis, comprehensive examination, professional experience, and residence requirements. Up to 12 graduate credits may be applied simultaneously to both the B.A. and M.A. programs or to both the B.S. and M.A. programs.

Students are considered as undergraduates until completion of 120 graduation credits and satisfactory completion of all B.A. or B.S. requirements. Upon meeting B.A. or B.S. requirements, students are automatically considered as graduate students.

Students may apply to the graduate committee of the department for admission to either combined program in mathematics at the beginning of their junior year or after the successful completion of 56 credits, but no later than the accumulation of 100 credits. A cumulative grade point average of 3.2 or higher and three supportive letters of recommendation from faculty are required for consideration.

## Combined Mathematics and Master of Business Administration Program:

In this program a student is able to obtain a B.S. degree in mathematics and a M.B.A. degree in a total of five years by taking a coordinated program in mathematics and business administration during the senior year. Application should be made during the second semester of the junior year to the director of the M.B.A. program, School of Business.

## Related Program

## Interdisciplinary Major in Computer Science and Applied Mathematics:

This major prepares a student to handle mathematically oriented computer applications in engineering and business. Details of the program are listed under Computer Science.

## Courses

A Mat 100 Precalculus Mathematics (3)

This course provides a background in those topics that are needed for success in calculus. Topics include graphing techniques, systems of equations, functions, logarithms, and trigonometry. May not be taken for credit by students with credit in any calculus course. Student with credit for the former A Mat 103 (College Algebra) may not take A Mat 100 for credit). Prerequisite(s): three years of high school mathematics or permission of department. May not be offered during 1998-99.

A Mat 101 Algebra and Calculus I (3)

An integrated approach to precalculus and calculus. Elements of algebra and analytic geometry necessary to study calculus of one variable. Functions, limits, continuity, differentiation of algebraic functions, applications of differentiation. May not be taken for credit by students with credit for A Mat 100, 106, 112 or 118. Prerequisite(s): three years of high school mathematics or permission of the department.

A Mat 102N Mathematics by Visualization (3)

Meets General Education: NS

This is a nontraditional course introducing contemporary mathematics primarily by visualization rather than algebra. This will enable the student to learn to see the way mathematicians see. Thus the student will be able to experience creative visualization in mathematics. The content of the course will include fractals; chaos; 4-dimensional geometry; Platonic solids; color maps; Escher tesselations. and impossible figures. A Mat 102F is the writing intensive version of A Mat 102N; only one of these may be taken for credit. Prerequisite(s): three years of high school mathematics or permission of instructor.

A Mat 102F Mathematics by Visualization (3)

Meets General Education: NS & WI

The course is writing intensive and each student will keep a journal (notebook). A Mat 102F is the writing intensive version of A Mat 102N; only one of these may be taken for credit. Prerequisite(s): three years of high school mathematics or permission of instructor.

A Mat 105 Finite Mathematics (3)

An introduction to topics of interest to students of the social sciences; sets and logic, partitions and counting, probability, vectors and matrices, theory of games. Prerequisite(s): three years of high school mathematics.

A Mat 106 Survey of Calculus (3)

An intuitive approach to differentiation and integration of algebraic and transcendental functions, intended only for students who plan to take no more calculus. Does not yield credit toward the major or minor in mathematics. May not be taken for credit by students with credit for A Mat 111, 112 or 118. Prerequisite(s): A Mat 100 or satisfactory performance on the mathematics placement exam.

A Mat 108 Elementary Statistics (3)

Frequency distributions, measures of central tendency and dispersion, probability and sampling, estimation, testing of hypotheses, linear regression and correlation. Prerequisite(s): three years of high school mathematics. Only one of A Mat 108 and B Msi 220 may be taken for credit.

A Mat 109 Applied Matrix Algebra (3)

Matrix algebra as applied to solving systems of linear equations. Markov chains, linear programming. Emphasizes calculations and applications rather than theory. Prerequisite(s): three years of high school mathematics.

A Mat 110 Introduction to Maple (2)

A hands-on introduction to the computer algebra system Maple. Basic commands are introduced by way of examples from the areas of algebra, calculus, number theory, graphics, business mathematics, and numerical analysis. Intended for transfer students having no background in Maple. Does not yield credit toward a major in mathematics. Prerequisite(s): A Mat 101 or a semester of calculus.

A Mat 111 Algebra and Calculus II (4)

The second semester of an integrated approach to precalculus and calculus; serves as a prerequisite to A Mat 113. Applications of differentiation, the definite integral, antiderivatives, logarithms, trigonometry, exponential functions. Only one of A Mat 111, 112 & 118 may be taken for credit. Prerequisite(s): A Mat 101.

A Mat 112 Calculus I (4)

Calculus of one variable. Limits, continuity, differentiation of algebraic functions, applications of differentiation, antiderivatives, the definite integral, transcendental functions. Prerequisite(s): A Mat 100 or satisfactory performance on the mathematics placement exam.

A Mat 113 Calculus II (4)

Techniques of integration, applications of the definite integral, conics, polar coordinates, improper integrals, infinite series. Prerequisite(s): A Mat 111 or 112.

A Mat 118 Honors Calculus I (4)

Honors version of first semester calculus. Same topics as A Mat 112, but topics are covered in greater depth. This course is for students with more than average ability and more than average interest in mathematics. Presidential Scholars with a strong interest in mathematics or the physical sciences should consider taking A Mat 118 instead of A Mat 112. A Mat 118 substitutes for A Mat 112 toward the prerequisite in any course. Only one of A Mat 112 & 118 may be taken for credit. Prerequisite(s): three years of secondary school mathematics and permission of the instructor. Offered fall semester only.

A Mat 119 Honors Calculus II (4)

Honors version of first semester calculus. Same topics as A Mat 113, but topics are covered in greater depth. This course is for students with more than average ability and more than average interest in mathematics. Presidential Scholars with a strong interest in mathematics or the physical sciences should consider taking A Mat 119 instead of A Mat 113. A Mat 119 substitutes for A Mat 113 toward the prerequisite in any course. Only one of A Mat 113 & 119 may be taken for credit. Prerequisite(s): A Mat 118, a grade ofAin A Mat 112, or permission of the instructor. Offered spring semester only.

A Mat 180 Calculus Seminar (1)

Topics in mathematics which involve calculus and either elaborate concepts from calculus or apply calculus to problems in other areas or disciplines. The seminar is intended for freshmen who have just completed one semester of calculus and wish to enrich their understanding of calculus. Prerequisite(s): one semester of calculus and permission of instructor.

A Mat 204 Actuarial Calculus and Linear Algebra (1)

Drill in problem solving in preparation for Course Exam 100 of the Society of Actuaries. Prerequisite(s): A Mat 214 and 220.S/Ugraded. Offered spring semester only.

A Mat 214 Calculus of Several Variables (4)

Curves and vectors in the plane, geometry of three-dimensional space, vector functions in three-space, partial derivatives, multiple integrals, line and surface integrals. Prerequisite(s): A Mat 113 or 119.

A Mat 220 Linear Algebra (3)

Linear equations, matrices, determinants, finite dimensional vector spaces, linear transformations Euclidean spaces. Prerequisite(s): A Mat 113 or 119.

A Mat 221 (same as A Csi 221) Introduction to Discrete Mathematics (3)

Topics chosen from sets, relations, induction, binomial theorem, permutations and combinations, counting, and related topics in discrete mathematics. Only one of A Mat 221 & A Csi 221 may be taken for credit. Prerequisite(s) or corequisite(s): A Mat 113 or 119.

A Mat 301 Theory of Interest (3)

The basic measures of interest, annuities, sinking funds, amortization schedules, bonds, and installment loans. Recommended as preparation for Course Exam 140 of the Society of Actuaries. Prerequisite(s): A Mat 113 or 119.

A Mat 308 Topics in Statistical Inference (3)

Various statistical techniques such as chi-square tests, multiple regression and correlation; nonparametric statistics, and the analysis of variance as applied to physical, biological, and social sciences. Prerequisite(s): A Mat 108. Offered spring semester only.

A Mat 311 Ordinary Differential Equations (3)

Linear differential equations, systems of differential equations, series solutions, boundary value problems, existence theorems, applications to the sciences. Prerequisite(s): A Mat 214.

A Mat 312 Basic Analysis (3)

Theoretical aspects of calculus including construction of the real numbers, differentiation and integration of functions in one variable, continuity, convergence, sequences and series of functions. A Mat 312Z is the writing intensive version of A Mat 312; only one may be taken for credit. Prerequisite(s): A Mat 214.

A Mat 312Z Basic Analysis (3)

Meets General Education: WI

A Mat 312Z is the writing intensive version of A Mat 312; only one may be taken for credit. Prerequisite(s): A Mat 214.

A Mat 313 Introduction to Numerical Methods (3)

Introduction to the theory and techniques in the numerical solution of mathematical problems. Topics include solutions of linear and nonlinear equations, interpolation, numerical integration, and numerical solution of differential equations. Only one of A Mat 313 or A Mat 401 may be taken for credit. Prerequisite(s): A Mat 220.

A Mat 314 Analysis for Applications I (3)

Introduction to topics in mathematical analysis which traditionally have been applied to the physical sciences, including vector analysis, Fourier series, ordinary differential equations, and the calculus of variations. Prerequisite(s): A Mat 214 and 220. Offered fall semester only.

A Mat 315 Analysis for Applications II (3)

Continuation of A Mat 314. Series solutions of differential equations, partial differential equations, complex variables, and integral transforms. Prerequisite(s): A Mat 314. Offered spring semester only.

A Mat 326 Classical Algebra (3)

Elementary number theory. Elementary theory of equations over rational, real, and complex fields. A Mat 326Z is the writing intensive version of A Mat 326; only one may be taken for credit. Prerequisite(s): A Mat 113 or 119.

A Mat 326Z Classical Algebra (3)

Meets General Education: WI

A Mat 326Z is the writing intensive version of A Mat 326; only one may be taken for credit. Prerequisite(s): A Mat 113 or 119.

A Mat 327 Elementary Abstract Algebra (3)

Basic concepts of groups, rings, integral domains, fields. A Mat 327Z is the writing intensive version of A Mat 327; only one may be taken for credit. Prerequisite(s): A Mat 220, and either 326 or 326Z.

A Mat 327Z Elementary Abstract Algebra (3)

Meets General Education: WI

A Mat 327Z is the writing intensive version of A Mat 327; only one may be taken for credit. Prerequisite(s): A Mat 220, and either 326 or 326Z.

A Mat 331 Transformation Geometry (3)

Classical theorems of Menelaus, Ceva, Desargues, and Pappus. Isometries, similarities, and affine transformations for Euclidean geometry. A Mat 331Z is the writing intensive version of A Mat 331; only one may be taken for credit. Prerequisite(s): A Mat 220. Offered spring semester only.

A Mat 331Z Transformation Geometry (3)

Meets General Education: WI

A Mat 331Z is the writing intensive version of A Mat 331; only one may be taken for credit. Prerequisite(s): A Mat 220. Usually offered spring semester.

A Mat 342 Elementary Topology (3)

Networks, map coloring problems, surfaces, topological equivalence, the Euler number, the polygonal Jordan curve theorem, homotopy, the index of a transformation, and the Brouwer Fixed Point Theorem. A Mat 342Z is the writing intensive version of A Mat 342; only one may be taken for credit. Prerequisite(s): A Mat 214 and 220. Offered fall semester only.

A Mat 342Z Elementary Topology (3)

Meets General Education: WI

A Mat 342Z is the writing intensive version of A Mat 342; only one may be taken for credit. Prerequisite(s): A Mat 214 and 220. Usually offered fall semester.

A Mat 367 Discrete Probability (3)

Introduction to combinatorial methods and discrete probability models. Binomial, Poisson, hypergeometric, negative binomial distributions. Selected classical problems; e.g., gamblers' ruin. Expected value and variance. Conditional probability. Weak law of large numbers and the central limit theorem. Optional topics; joint probability mass functions, correlations, Markov chains. Mat 367Z is the writing intensive version of Mat 367; only one may be taken for credit.

A Mat 367Z Discrete Probability (3)

Meets General Education: WI

Writing intensive version of A Mat 367; only one of the two courses may be taken for credit. Prerequisite(s): A Mat 113 or 119 plus 6 credits at the 200 level or above in either mathematics or computer science.

A Mat 368 Statistics and Continuous Probability (3)

Continuous random variables, including the normal, exponential, t, and chi-square. Maximum likelihood and unbiased estimators. Confidence intervals and hypothesis tests, mainly for normal means and variances, based on one and two samples. F distribution. Behrens-Fisher problem. May not be taken for credit by students with credit for Mat 362 or Mat 362Z. Mat 368Z is the writing intensive version of Mat 368; only one of Mat 368 and Mat 368Z may be taken for credit. Prerequisite(s): A Mat 367 or A Mat 367Z.

A Mat 368Z Statistics and Continuous Probability (3)

Meets general education: WI

Writing intensive version of A Mat 368; only one may be taken for credit. Mat 368Z may not be taken for credit by students with credit for Mat 362 or Mat 362Z. Prerequisite(s): A Mat 367 or A Mat 367Z.

A Mat 369 Statistics and Data Analysis (3)

Continuation of Mat 368. Chi-squared tests for goodness-of-fit and for independence. Introduction to regression. Analysis of variance. Distribution free methods. Robustness, transformations of data. Students will use a statistical computer package (usually Minitab), no prior knowledge of which is assumed. The course will normally be taught in a computer classroom. Normally offered spring semester only. Prerequisite(s): A mat 368 or A Mat 368Z and A Mat 214.

A Mat 372 Linear Programming and Game Theory (3)

Operation and theory of the simplex algorithm for solving linear programming problems, duality theory, and matrix games. A Mat 372Z is the writing intensive version of A Mat 372; only one may be taken for credit. Prerequisite(s): A Mat 109 or 220. Offered fall semester only.

A Mat 372Z Linear Programming and Game Theory (3)

Meets General Education: WI

A Mat 372Z is the writing intensive version of A Mat 372; only one may be taken for credit. Prerequisite(s): A Mat 109 or 220. Usually offered fall semester.

A Mat 374 Operations Research (3)

Operations research techniques and applications, linear programming, queuing theory, including birth and death processes, decision theory, network analysis, simulation. Recommended as preparation for Course Exam 130 of the Society of Actuaries. Prerequisite(s): A Mat 367 or 367Z or permission of instructor. Offered spring semester only.

A Mat 401 Numerical Analysis (3)

Error analysis, numerical solution of nonlinear equations, interpolation and polynomial approximation, numerical differentiation and integration, direct methods for solving linear systems. Recommended as preparation for Course Exam 135 of the Society of Actuaries. Not more than one of A Mat 313 or A Mat 401 may be taken for credit. Prerequisite(s): A Mat 220. Offered fall semester only.

A Mat 403A Life Contingencies (3)

Treatment of the contingencies of a single life including: mortality functions, life annuities, life insurance functions, annual premiums, net level premium reserves, the expense factor, and more complex benefits. Prerequisite(s): A Mat 301, 367.

A Mat 403B Life Contingencies (3)

Expansion of Mat 403A with emphasis on two or more lives in combination and on multiple causes of decrement. Topics include population theory, multi-life statuses, multi-life functions, reversionary annuities, multiple-decrement functions, primary and secondary decrements, and applications of multiple-decrement functions. Prerequisite(s): A Mat 403A.

A Mat 409 Vector Analysis (3)

Classical vector analysis presented heuristically and in physical terms. Topics include the integral theorems of Gauss, Green, and Stokes. Prerequisite(s): A Mat 214. Offered spring semester only.

A Mat 412 Complex Variables for Applications (3)

The elementary functions, differentiation, conformal transformations, power series, integral theorems, Taylor's theorems, Taylor's and Laurent's expansions, applications of residues. A Mat 412Z is the writing intensive version of A Mat 412; only one may be taken for credit. Prerequisite(s): A Mat 214. Offered fall semester only.

A Mat 412Z Complex Variables for Applications (3)

Meets General Education: WI

A Mat 412Z is the writing intensive version of A Mat 412; only one may be taken for credit. Prerequisite(s): A Mat 214. Usually offered fall semester.

A Mat 413 & 413Z, and 414 Advanced Calculus (3, 3)

Meets General Education: WI (A Mat 413Z only)

A rigorous presentation of the traditional topics in the calculus of several variables and their applications. Topics include the implicit function theorem, Taylor's theorem, Lagrange multipliers, Stieltjes integral, Stokes' theorem, infinite series, Fourier series, special functions, Laplace transforms. A Mat 413Z is the writing intensive version of A Mat 413, only one may be taken for credit. Prerequisite(s): A Mat 312 or 312Z; A Mat 413 or 413Z is a prerequisite for 414.

A Mat 416 Partial Differential Equations (3)

The partial differential equations of classical mathematical physics. Separation of variables, eigenvalue problems, Fourier series and other orthogonal expansions. First order equations, Green's functions, Sturm-Liouville theory, and other topics as time permits. Prerequisite(s): a course in Ordinary Differential Equations. Offered fall semester only.

A Mat 420 Abstract Algebra (3)

Topics in group theory, especially finite group theory, algebraic field extensions, and Galois theory. Prerequisite(s): A Mat 327 or 327Z.

A Mat 424 Advanced Linear Algebra (3)

Duality, quadratic forms, inner product spaces, and similarity theory of linear transformations. Prerequisite(s): A Mat 220. Offered fall semester only.

A Mat 425 Number Theory (3)

Divisibility, congruencies, quadratic reciprocity, Diophantine equations, sums of squares, cubes, continued fractions, algebraic integers. Prerequisite(s): A Mat 326 or 326Z. Offered spring semester only.

A Mat 432 Foundations of Geometry (3)

Axiomatic development of absolute geometry, theory of parallels, introduction to non-Euclidean geometry, isometries of the Bolyai-Lobachevsky plane. A Mat 432Z is the writing intensive version of A Mat 432; only one may be taken for credit. Prerequisite(s): A Mat 220. Offered fall semester only.

A Mat 432Z Foundations of Geometry (3)

Meets General Education: WI

A Mat 432Z is the writing intensive version of A Mat 432; only one may be taken for credit. Prerequisite(s): A Mat 220. Normally only the writing intensive version of this course is offered.

A Mat 441 Introduction to Differential Geometry (3)

Differential geometry of curves and surfaces in Euclidean space, frames, isometries, geodesics, curvature, and the Gauss-Bonnet theorem. Prerequisite(s): A Mat 214 and 220. Offered fall semester only.

A Mat 442 Introduction to Algebraic Topology(3)

Two dimensional manifolds, the fundamental group and Van Kampen's theorem, covering spaces, graphs, and applications to group theory. Prerequisite(s): A Mat 214 and 220.

A Mat 452 History of Mathematics (3)

History of the development of mathematics, emphasizing the contributions of outstanding persons and civilizations. A Mat 452Z is the writing intensive version of A Mat 452; only one may be taken for credit. Prerequisite(s): A Mat 214, 326 or 326Z, and either 331 or 331Z or 432 or 432Z. Normally only the writing intensive version of this course is offered.

A Mat 452Z History of Mathematics (3)

Meets General Education: WI

A Mat 452Z is the writing intensive version of A Mat 452; only one may be taken for credit. Prerequisite(s): A Mat 214, 326 or 326Z, and either 331 or 331Z or 432 or 432Z. Offered fall semester only.

A Mat 464 Applied Stochastic Processes (3)

An overview of various stochastic processes found in practice with particular emphasis on Markov chains. Introduction to queuing theory. Particular attention given to estimation. Examples of applications. Prerequisite(s): A Mat 367 or 367Z or 467. Offered spring semester only.

A Mat 465 Applied Statistics (3)

A second or third course in statistics. Central theme is forecasting; i.e., simple and multiple regression and time series. Recommended as preparation for Course Exam 120 of the Society of Actuaries. A Mat 465Z is the writing intensive version of A Mat 465; only one may be taken for credit. Normally offered only in fall semesters. Prerequisite(s): A Mat 220 and either A Mat 368 or A Mat 468.

A Mat 465Z Applied Statistics (3)

Meets General Education: WI

Writing intensive version of A Mat 465; only one of the two courses may be taken for credit. Prerequisite(s): A Mat 220 and either A Mat 368 or A Mat 468.

A Mat 467 Continuous Probability and Mathematical Statistics (3)

One and two dimensional calculus applied to probability. Continuous random variables in one and two dimensions, including the normal, bivariate normal, exponential, gamma (including chi- square) and beta. Density functions of transformations of random variables. Moment generating functions, weak law of large numbers, central limit theorems, convergence of random variables. Maximum likelihood and unbiased estimators. Confidence intervals, mainly for normal means and variances. Mat 467 and 468 are designed to prepare students for the Course 110 examination of the Society of Actuaries. Prerequisite(s): A Mat 367 or Mat 367Z, Mat 214 and Mat 220. Offered fall semester only.

A Mat 468 Mathematical Statistics (3)

Neyman-Pearson theory (hypothesis testing), type I and II errors, power functions, generalized likelihood ratio tests. Two-sample confidence intervals and hypothesis tests. Sampling distributions, including the t, chi-square and F, all rigorously defined. Sufficient statistics, Fisher information, minimum variance estimators. Introduction to regression. Prerequisite: A Mat 467. Offered spring semester only.

A Mat 469 Actuarial Probability and Statistics (1)

Drill in problem solving in preparation for Course Exam 110 of the Society of Actuaries. Prerequisite(s): A Mat 468 or taken concurrently with A Mat 468.S/Ugraded. Offered spring semester only.

A Mat 481A and B Senior Seminar (3, 3)

Study of topics in mathematics, chosen at the discretion of the instructor. Prerequisite(s): permission of instructor.

A Mat 497 Independent Study in Mathematics (1-3)

Individual, independent study of selected topics not covered in a regularly scheduled course. Open only to majors in mathematics. May be repeated for credit. Prerequisite(s): junior or senior class standing, and permission of instructor with whom student wishes to study.

A Mat 499Z Undergraduate Thesis (3)

Individual, independent study leading to an undergraduate thesis under the direction of faculty chosen by the student. The thesis may be used to fulfill the thesis requirement in the honors program with the approval of the department. Prerequisite(s): permission of instructor.

Undergraduate Bulletin — Table of Contents

University at Albany

State University of New York