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Mathematics

Department of Mathematics

College of Arts and Sciences
244 Mathematics Building
North Campus
Buffalo, NY 14260

Phone: 716.645.6284
Fax: 716.645.5039
Web: www.math.buffalo.edu

Samuel D. Schack
Chair

John Ringland
Director of Undergraduate Studies
UndergraduateStudies@math.buffalo.edu

About the Program

Mathematics is a broad discipline with many diverse applications in social, managerial, and life sciences, as well as in the physical sciences and engineering. The Department of Mathematics provides a variety of concentrations leading to a baccalaureate degree.

Degree Options

B.A. in Mathematics
General Curriculum in Mathematics
Basic liberal arts major program in mathematics; not tied to a specific career direction, but rather provides a general background for students interested in a variety of careers that require mathematical expertise.

Concentration C
Mathematics major with a concentration in computing and applied mathematics; designed for students interested in careers in applying mathematics or doing scientific programming.

Concentration GS/ED
For the student whose career goal is to attain a master's degree for professional certification in adolescent mathematics education; may be coupled with a minor in teacher education.

Concentration GS
Basic theoretical course of study for mathematics majors intending graduate study in mathematics, or intending careers in such fields as actuarial science, financial analysis or cryptography.

Concentration GS/AM
Mathematics major for intended graduate study in applied mathematics; a basic theoretical course of study for students planning a career and/or graduate study in applied mathematics.

BS in Mathematics
Concentration BSc
Same as Program GS with four additional electives.

Concentration BSc/AM
Same as Program GS/AM with four additional electives.

BA in Mathematics/Economics
Program M/E
Joint major with economics, for students intending graduate study in economics.

BS in Mathematical Physics
Program M/P
Joint major with physics, for students intending graduate study in mathematical physics.

BS in Bioinformatics and Computational Biology
Concentration in Mathematics
The university offers a bachelor of science degree in bioinformatics and computational biology, with options for a concentration in biology, biophysics, computer science and engineering, or mathematics. Please refer to the Bioinformatics and Computational Biology program for further details.

BA/MA in Mathematics
Five-year, 138-credit combined degree program. Admission requires a minimum GPA of 3.0 in courses through differential equations and linear algebra, as well as letters of recommendation. For program details, contact the director of undergraduate studies.

Acceptance Information

Applicants to the mathematics program should bring a copy of their current UB DARS reports directly to the Department of Mathematics. Students may apply at any time after they have completed the three-course calculus sequence MTH 141-MTH 142-MTH 241 or the equivalent at a transfer institution, but should apply, if possible, while enrolled in MTH 241 to receive appropriate advisement.

The department�s requirement for admission is a minimum GPA of 2.5 in the three calculus courses. Students who have taken more than these three courses usually need a minimum grade of C in any additional required courses they have completed.

Note: Admittance to the department guarantees admittance to the General Curriculum Program only�all other concentrations or programs require specific approval from the director of undergraduate studies. Students who expect difficulty in being admitted to the department should follow the requirements for the General Curriculum Program or see the director of undergraduate studies for advice on which concentration to follow, pending admittance.

Advisement

Students, including freshmen, who are considering majoring in mathematics are encouraged to consult as early as possible with the departmental director of undergraduate studies. Admission to the department as far in advance of graduation as possible ensures that the department and the student can plan together a program best suited to the student�s needs.

Admission Advisement. Note: If you are majoring in mathematics, see the director of undergraduate studies at least once a year. If you are intending to major in mathematics, contact the director of undergraduate studies as soon as possible regarding your program. Even if your grades are too low for acceptance to the department, you should see the director of undergraduate studies regarding conditions for acceptance and suggestions for your schedule while waiting for admittance.

The Department of Mathematics provides academic advice to majors and non-majors. The Office of Undergraduate Studies is open 9:00 a.m.�5:00 p.m., Monday�Friday. Students in need of advisement on acceptance to the department, choice of courses, program or degree decisions, or career advisement, should see the director of undergraduate studies.

Upon acceptance to the department, it is recommended that students meet with the director of undergraduate studies to map out their programs. Students in all concentrations except computing and applied math are required to discuss with the undergraduate director the appropriateness of their choice of program; this is an opportunity for students to clarify their understanding of the more theoretically oriented programs.

Course Advisement. MTH 115 Survey of Algebra and Trigonometry or three years of high school math is a prerequisite for the freshman calculus course. Students whose mathematical preparation is so weak that they are not prepared for MTH 115 are encouraged to take courses in the university�s Learning Center, located in 217 Baldy Hall.

The Department of Mathematics offers four calculus sequences:
(1) MTH 141-MTH 142-MTH 241 College Calculus I-III: the standard basic calculus course for engineering and science (including computer science) students. It is a prerequisite for more advanced work in mathematics.
(2) MTH 121-MTH 122 Survey of Calculus and Applications I-II: a basic calculus course for general health sciences, and arts and letters. It is somewhat easier than MTH 141-MTH 142 and does not go into the subject as deeply. MTH 121-MTH 122 does not meet the requirements of most science majors.
(3) MTH 131 Mathematical Analysis for Management: a one semester calculus course for management students. It meets the calculus requirement for students in the School of Management.
(4) MTH 153-MTH 154 Honors Calculus I-II: emphasizes proofs and concepts of calculus.

Students who are unsure whether to take MTH 141-MTH 142 or MTH 121-MTH 122 should take MTH 141-MTH 142. Taking MTH 121-MTH 122 might delay graduation by as much as a year.

Since each of the calculus sequences has its own specific requirements and purpose, a change in sequence (MTH 121-MTH 122 or MTH 141-MTH 142) is not recommended. Students who take MTH 121 and later decide that they need to switch into the MTH 141-MTH 142 track will usually need to take MTH 141 first, since even a good grasp of MTH 121 can fail to provide adequate preparation for MTH 142.

Students taking freshman mathematics courses can get tutoring help on a drop-in basis from the Mathematics Help Center. This facility is located in 107 and 110 Mathematics Building.

Recommendations Concerning Related Courses. The Department of Mathematics strongly recommends that its majors in the theoretically oriented concentrations (Concentrations GS and GS/AM or Concentrations BSc and BSc/AM) take at least two semesters of French, German, or Russian, since these, along with English, are the basic languages of the mathematical literature.

All mathematicians need some facility with computers; the department, therefore, recommends that its students take an introductory course in scientific programming. Specifically, a one-year sequence, CSE 113-CSE 114 or CSE 115-CSE 116, is strongly recommended for students majoring in mathematics. Some major concentrations have specific computer science requirements.

Academic Requirements

Departmental Probation. Students whose math GPA drops below 2.0 are placed on departmental probation for one semester. If their GPA remains below 2.0 at the end of the probationary semester, they are dropped from the department. They may reapply after one semester.

Departmental Requirements for Graduation. After a student has been accepted as a major, progress toward fulfillment of the degree requirements is monitored by the department. A student is recommended for a baccalaureate degree in mathematics only if:
(1) the program has been approved by the director of undergraduate studies,
(2) all required/approved courses have been completed, and
(3) a minimum departmental GPA of 2.0 has been attained in the specific program.

Transfer Policy

Transfer students who intend to major in mathematics are urged to consult the director of undergraduate studies before or very early in their first semester at the University at Buffalo to determine equivalency of transferred mathematics courses. Transfer students are required to complete at least four upper-division courses in the Department of Mathematics at the University at Buffalo.

Mathematics - B.S.

Concentration BSc: General Study in Mathematics

About the Concentration

This concentration provides a basic theoretical course of study for mathematics majors intending graduate study in mathematics. Admission to this concentration is by departmental approval only. See the director of undergraduate studies regarding approval.

Acceptance Criteria

Minimum GPA of 2.5 in the prerequisite courses.

Prerequisite Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
MTH 241 College Calculus III

Required Courses

MTH 311 Introduction to Higher Mathematics
MTH 306 Introduction to Differential Equations
MTH 309 Introductory Linear Algebra
MTH 419 Introduction to Algebra I
MTH 420 Introduction to Algebra II
MTH 431 Introduction to Real Variables I
MTH 432 Introduction to Real Variables II
Three 300/400-level mathematics courses (not MTH 417)
Four 300/400-level courses in mathematics or computer science (not MTH 417)

Summary
Total required credit hours for the major (concentration BSc): 64-68

See Baccalaureate Degree Requirements for general education and remaining university requirements.

Recommended Sequence of Program Requirements

FIRST - THIRD YEARS
Follow first three years of concentration GS

FOURTH YEAR
Three 300/400 - level mathematics courses (not MTH 417)
Four 300/400 - level courses in mathematics or computer science (not MTH 417)

Note: Not all seven electives need to be taken in the senior year.

Mathematics - B.S.

Concentration BSc/AM: General Study in Applied Mathematics

About the Concentration

This concentration provides a course of study for mathematics majors intending to pursue graduate study in applied mathematics. Admission to this concentration is by departmental approval only. See the director of undergraduate studies regarding approval.

Acceptance Criteria

Minimum GPA of 2.5 in the prerequisite courses.

Prerequisite Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
MTH 241 College Calculus III

Required Courses

CSE 115 Introduction to Computer Science for Majors I
CSE 116 Introduction to Computer Science for Majors II
MTH 306 Introduction to Differential Equations
MTH 309 Introductory Linear Algebra
MTH 311 Introduction to Higher Mathematics
MTH 418 Survey of Partial Differential Equations or MTH 449 Introduction to Partial Differential Equations
MTH 419 Introduction to Algebra I or MTH 420 Introduction to Algebra II
MTH 431 Introduction to Real Variables I
MTH 432 Introduction to Real Variables II
Three 300/400-level mathematics courses (not MTH 417)
Four 300/400-level courses in mathematics or computer science (not MTH 417)
PHY 107 General Physics I
PHY 108 General Physics II

Summary
Total required credit hours for the major (concentration BSc/AM): 77-83

See Baccalaureate Degree Requirements for general education and remaining university requirements.

Recommended Sequence of Program Requirements

FIRST YEAR
Fall�CSE 115, MTH 141, PHY 107
Spring�CSE 116, MTH 142, PHY 108

SECOND YEAR
Fall�MTH 241, MTH 309
Spring�MTH 306, MTH 311

THIRD YEAR
Fall�MTH 418 or MTH 449; MTH 431
Spring�MTH 419 or MTH 420; MTH 432

FOURTH YEAR
Three 300/400-level mathematics courses (not MTH 417)
Four 300/400-level courses in mathematics or computer science (not MTH 417)

Note: Not all seven electives need to be taken in the senior year.

Mathematical Physics - B.S.

Acceptance Criteria

Minimum GPA of 2.5 in the prerequisite courses.

Advising Notes

Students should consult with the undergraduate director in each department regarding approved electives.

This is a joint program. A student who follows this program but does not complete it will have difficulty completing a math major without substantial additional coursework.

Prerequisite Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
PHY 107 General Physics I or PHY 117 Honors Physics I
PHY 108 General Physics II or PHY 118 Honors Physics II
PHY 158 General Physics II Lab

Required Courses

MTH 241 College Calculus III
MTH 306 Introduction to Differential Equations
MTH 309 Introductory Linear Algebra
MTH 417 Survey of Multivariable Calculus
MTH 418 Survey of Partial Differential Equations
MTH 419 Introduction to Algebra I or MTH 420 Introduction to Algebra II
MTH 424 Fourier Series
MTH 425 Introduction to Complex Variables I
PHY 207 General Physics III or PHY 217 Honors Physics III
PHY 208 General Physics IV
PHY 257 General Physics III Lab
PHY 301 Intermediate Mechanics I
PHY 307 Modern Physics Lab
PHY 401 Modern Physics I
PHY 403 Electricity and Magnetism I
PHY 405 Thermal and Statistical Physics I
PHY 407 Advanced Laboratory or PHY 408 Advanced Laboratory
One 300/400-level MTH elective
One PHY elective (one of the following: PHY 302 Intermediate Mechanics II, PHY 402 Modern Physics II, PHY 404 Electricity and Magnetism II, or PHY 406 Thermal and Statistical Physics II)

Summary
Total required credit hours for the major: 81

See Baccalaureate Degree Requirements for general education and remaining university requirements.

Recommended Sequence of Program Requirements

FIRST YEAR
Fall�MTH 141
Spring�MTH 142; PHY 107 or PHY 117

SECOND YEAR
Fall�MTH 241; PHY 108 or PHY 118; PHY 158
Spring�MTH 306, MTH 309; PHY 207 or PHY 217; PHY 208, PHY 257

THIRD YEAR
Fall�MTH 417, PHY 301, PHY 307, PHY 401
Spring�MTH 418, one PHY elective

FOURTH YEAR
Fall�MTH 419 or MTH 420; MTH 425, PHY 403, PHY 405
Spring�MTH 424; PHY 407 or PHY 408; one 300/400-level MTH elective

Mathematics - B.A.

General Curriculum in Mathematics

General Curriculum in Mathematics

This is the basic liberal arts major program in mathematics, and allows for freedom in course choice by the students. A total of nine mathematics (MTH) courses are required: four core courses (MTH 141, MTH 142, MTH 241, MTH 309) generally completed in the first two years, and five electives. Several concentrations requiring additional coursework are available for students with specific career goals.

Acceptance Criteria

Minimum GPA of 2.5 in the prerequisite courses (or transfer equivalents).

Prerequisite Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
MTH 241 College Calculus III

Required Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
MTH 241 College Calculus III
MTH 309 Introduction to Linear Algebra
One of the following: MTH 306 Introduction to Differential Equations, MTH 337 Introduction to Scientific Computing, MTH 437 Introduction to Numerical Analysis I, or other computer applications course approved by the director of undergraduate studies in mathematics
One of the following: MTH 311 Introduction to Higher Mathematics, MTH 313 Elements of Set Theory, MTH 335 Elements of Geometry, MTH 419 Introduction to Algebra I, MTH 420 Introduction to Algebra II, MTH 431 Introduction to Real Variables I, or other proofs course approved by the director of undergraduate studies in mathematics
Three 300/400-level mathematics courses

Summary
Total required credit hours for the major (basic curriculum): 33-36
(nine courses in mathematics)

See Baccalaureate Degree Requirements for general education and remaining university requirements.

Recommended Sequence of Program Requirements

FIRST YEAR
Fall�MTH 141
Spring�MTH 142

SECOND YEAR
Fall�MTH 241
Spring�MTH 309

THIRD YEAR
Fall�One of the following: MTH 306, MTH 337, MTH 437, or other computer applications course approved by the director of undergraduate studies in mathematics
Spring�One of the following: MTH 311, MTH 313, MTH 335, MTH 419, MTH 420, MTH 431, or other mathematical proofs course approved by the director of undergraduate studies in mathematics
(Note: selections above must be made in consultation with the director of undergraduate studies in mathematics.)

FOURTH YEAR
Fall and Spring�Three 300/400 level-mathematics courses

Each elective must be pre-approved by the director of undergraduate studies in mathematics

Mathematics - B.A.

Concentration C: Computing and Applied Mathematics

About the Concentration

This concentration is designed to serve those students interested in careers as applied mathematicians or scientific applications programmers.

The courses in this concentration are like the calculus and computing courses, though more difficult. A student who can handle MTH 141, MTH 142, MTH 241, CSE 115, and CSE 116 should be able to handle concentration C.

Acceptance Criteria

Minimum GPA of 2.5 in the prerequisite courses.

Prerequisite Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
MTH 241 College Calculus III

Required Courses

CSE 115 Introduction to Computer Science for Majors I
CSE 116 Introduction to Computer Science for Majors II
CSE 241 Digital Systems
CSE 250 Algorithms and Data Structures
MTH 306 Introduction to Differential Equations
MTH 309 Introductory Linear Algebra
MTH 417 Survey of Multivariable Calculus and MTH 418 Survey of Partial Differential Equation or MTH 431 Introduction to Real Variables I and MTH 432 Introduction to Real Variables II*
MTH 437 Introduction to Numerical Analysis I
MTH 438 Introduction to Numerical Analysis II
Two 300/400-level mathematics courses
Two 300/400-level courses in mathematics or computer science

Summary
Total required credit hours for the major (concentration C): 64-68

See Baccalaureate Degree Requirements for general education and remaining university requirements.

Recommended Sequence of Program Requirements

FIRST YEAR
Fall�CSE 115, MTH 141
Spring�CSE 116, MTH 142

SECOND YEAR
Fall�CSE 241, MTH 241
Spring�CSE 250, MTH 306

THIRD YEAR
Fall�MTH 309; MTH 417 or MTH 431*
Spring�MTH 418 or MTH 432*

FOURTH YEAR
Fall�MTH 437
Spring�MTH 438
Fall or Spring�Two 300/400-level mathematics courses, two 300/400-level courses in mathematics or computer science

*MTH 311 is a prerequisite for MTH 431. Students must take one complete sequence MTH 417-MTH 418 or MTH 431-MTH 432. Students intending to go to graduate school in applied mathematics should take MTH 311-MTH 431-MTH 432 instead of MTH 417-MTH 418. MTH 311 would then count as a technical elective.

Approved Technical Electives Recommended

MTH 314, MTH 343, MTH 353, MTH 354, MTH 411, MTH 412, MTH 424, MTH 425, MTH 426, MTH 443, MTH 444, MTH 445, MTH 449, MTH 460, MTH 463

Any other 300/400-level MTH course would also be acceptable. MTH 311 may be taken as an elective; it is the first abstract theoretical course with proofs. Note that MTH 431-MTH 432 and MTH 419-MTH 420 are designed for students who want intensive preparation in analysis and modern algebra, and are not good choices to just fill out their schedule. MTH 431-MTH 432 may be taken as electives (in addition to MTH 417 or MTH 418) or as requirements (in place of MTH 417 and MTH 418).

Approved technical electives outside the Mathematics department: CSE 305, 400-level CSE courses

Mathematics - B.A.

Concentration GS: General Study in Mathematics

About the Concentration

This concentration describes a basic theoretical course of study for mathematics majors intending to pursue graduate study in mathematics, or intending careers in such fields as actuarial science, financial analysis, or cryptography.

Admission to this concentration is by departmental approval only. See the director of undergraduate studies regarding approval.

Acceptance Criteria

Minimum GPA of 2.5 in the prerequisite courses.

Advising Notes

Concentration GS has the fewest courses of any of the math concentrations except General Curriculum, but many courses are quite difficult; MTH 311, MTH 431-MTH 432, and MTH 419-MTH 420 are abstract theoretical courses emphasizing proofs. A student must do well in MTH 311 to enter this program.

Students planning to go to graduate school should meet with the director of undergraduate studies in mathematics in the fall semester of their junior year. They should plan to take the GREs in either spring of the junior year or fall of the senior year.

Prerequisite Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
MTH 241 College Calculus III

Required Courses

MTH 306 Introduction to Differential Equations
MTH 309 Introductory Linear Algebra
MTH 311 Introduction to Higher Mathematics
MTH 419 Introduction to Algebra I
MTH 420 Introduction to Algebra II
MTH 431 Introduction to Real Variables I
MTH 432 Introduction to Real Variables II
One 300/400-level mathematics course (not MTH 417)
Two 300/400-level courses in mathematics or computer science (not MTH 417)

Summary
Total required credit hours for the major (concentration GS): 49-52
(thirteen courses in math and related areas)

See Baccalaureate Degree Requirements for general education and remaining university requirements.

Recommended Sequence of Program Requirements

FIRST YEAR
Fall�MTH 141
Spring�MTH 142

SECOND YEAR
Fall�MTH 241, MTH 309
Spring�MTH 306, MTH 311

THIRD YEAR
Fall�MTH 419, MTH 431
Spring�MTH 420, MTH 432

FOURTH YEAR
Fall or Spring�One 300/400-level mathematics course (not MTH 417), two 300/400-level courses in mathematics or computer science (not MTH 417)

Mathematics - B.A.

Concentration GS/AM: General Study in Applied Mathematics

About the Concentration

This concentration describes a course of study for mathematics majors intending to pursue graduate study in applied mathematics. Admission to this concentration is by departmental approval only. See the director of undergraduate studies regarding approval.

Acceptance Criteria

A minimum GPA of 2.5 in the prerequisite courses.

Advising Notes

MTH 311-MTH 431-MTH 432 and MTH 419 are abstract theoretical courses emphasizing proofs. A student must do well in MTH 311 to enter this program.

Students planning to go to graduate school should meet with the director of undergraduate studies in mathematics in the fall semester of their junior year. They should plan to take the GREs in either spring of the junior year, or fall of the senior year.

Prerequisite Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
MTH 241 College Calculus III

Required Courses

CSE 115 Introduction to Computer Science for Majors I
CSE 116 Introduction to Computer Science for Majors II
MTH 306 Introduction to Differential Equations
MTH 309 Introductory Linear Algebra
MTH 311 Introduction to Higher Mathematics
MTH 418 Survey of Partial Differential Equations or MTH 449 Introduction to Partial Differential Equations
MTH 419 Introduction to Algebra I or MTH 420 Introduction to Algebra II
MTH 431 Introduction to Real Variables I
MTH 432 Introduction to Real Variables II
Three 300/400-level courses in mathematics or computer science (not MTH 417)
PHY 107 General Physics I
PHY 108 General Physics II

Summary
Total required credit hours for the major (concentration GS/AM): 65-67
(seventeen courses in math and related areas)

See Baccalaureate Degree Requirements for general education and remaining university requirements.

Recommended Sequence of Program Requirements

FIRST YEAR
Fall�CSE 115, MTH 141, PHY 107
Spring�CSE 116, MTH 142, PHY 108

SECOND YEAR
Fall�MTH 241, MTH 309
Spring�MTH 306, MTH 311

THIRD YEAR
Fall�MTH 419 or MTH 420; MTH 431
Spring�MTH 418 or MTH 449; MTH 432

FOURTH YEAR
Fall or Spring�Three 300/400-level courses in mathematics or computer science (not MTH 417)

Mathematics - Economics - B.A.

Program M/E: Joint Major in Mathematics/Economics

About the Concentration

This is a program for students intending graduate study in economics. Acceptance into this program requires a minimum GPA of 2.5 in both the mathematics and economics courses during the first year. Separate applications must be submitted to both the Department of Mathematics and the Department of Economics. Admission to this program is by departmental approval only. See the director of undergraduate studies regarding approval.

Acceptance Criteria

A minimum GPA of 2.5 in the prerequisite courses.

Advising Notes

A student must be able to handle MTH 311 to enter this program. Students should consult the advisor in each department concerning senior-level courses. Exceptions in the curriculum may be allowed through consultation with the appropriate department. Interested students should contact the departments upon application for up-to-date information on possible changes.

Prerequisite Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
MTH 241 College Calculus III

Required Courses

ECO 405 Microeconomic Theory
ECO 407 Macroeconomic Theory or ECO 337 Honors Macroeconomic Theory
MTH 306 Introduction to Differential Equations
MTH 309 Introductory Linear Algebra
MTH 311 Introduction to Higher Mathematics
MTH 411 Probability Theory
MTH 412 Introduction to Statistical Inference
MTH 419 Introduction to Algebra I or MTH 420 Introduction to Algebra II
MTH 431 Introduction to Real Variables I
One 300/400-level mathematics course (not MTH 417)
Two 300/400-level courses in economics (not ECO 480 or ECO 481)

Summary
Total required credit hours for the major (program M/E): 58-61
(fifteen courses in math and economics)

See Baccalaureate Degree Requirements for general education and remaining university requirements.

Recommended Sequence of Program Requirements

FIRST YEAR
Fall�MTH 141
Spring�MTH 142

SECOND YEAR
Fall�ECO 407 or ECO 337; MTH 241
Spring�ECO 405, MTH 306, MTH 309, MTH 311

THIRD YEAR
Fall�MTH 411, MTH 431
Spring�MTH 412; MTH 419 or MTH 420

FOURTH YEAR
Fall or Spring�One 300/400-level mathematics course (not MTH 417), two 300/400-level courses in economics (not ECO 480 or ECO 481)

Mathematics - B.A.

Concentration GS/ED: General Study in Mathematics and Education

About the Concentration

This concentration is designed for the student whose career goal is to attain a master�s degree for professional certification in adolescent mathematics education. Students interested in this concentration should obtain advisement from the director of undergraduate studies in mathematics, 233 Mathematics Building, and, for questions related to the education courses, from the Teacher Education Institute (TEI), 375 Baldy Hall.

Admission to the major must be sought from the Department of Mathematics, usually in the student�s second year. For advice on prerequisites for required courses in education and selection of general education courses fulfilling the State Education Department (SED) requirement for prospective teachers, students should consult with TEI as early as their freshman year.

Completion of the major concentration (including the required education courses) provides advanced status toward initial New York State teacher certification, accomplished through one year of subsequent coursework at the graduate level through the Graduate School of Education. It is then possible to complete, within the state-mandated three years, the master�s degree required for a professional teaching certificate, provided that all NYS requirements have been successfully completed.

Acceptance Criteria

A minimum GPA of 2.5 in the prerequisite courses.

Advising Notes

The courses in this concentration are more theoretical than those in concentration C; MTH 311, MTH 419, and MTH 431 are difficult. A student must be able to handle MTH 311 in order to enter this concentration. Warning: In order to graduate with a degree in mathematics in concentration GS/ED, a student must complete all the required education courses, as well as the required mathematics courses. Students who complete concentration GS/ED math requirements but do not complete the education requirements must change to the basic curriculum or to another concentration in order to graduate. It is recommended that students interested in this concentration contact the department upon application for up-to-date information on possible changes in requirements.

Prerequisite Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
MTH 241 College Calculus III

Required Courses

CEP 400 Educational Psychology
CSE 113 Introduction to Computer Science I or CSE 115 Introduction to Computer Science for Majors I
CSE 114 Introduction to Computer Science II or CSE 116 Introduction to Computer Science for Majors II
ELP 405 Sociology of Education
LAI 350 Introduction to Education
LAI 414 Language, Cognition & Writing
MTH 191/CSE 191 Introduction to Discrete Mathematics
MTH 306 Introduction to Differential Equations
MTH 309 Introductory Linear Algebra
MTH 311 Introduction to Higher Mathematics
MTH 335 Elements of Geometry
MTH 411 Probability Theory
MTH 419 Introduction to Algebra I
MTH 431 Introduction to Real Variables I
One 300/400-level mathematics elective (not MTH 417)
Two 300/400-level electives from the Educational Leadership and Policy department or the Counseling, School, and Educational Psychology department, or one education-related College of Arts and Sciences course

Summary
Total required credit hours for the major: 74-75
(fourteen courses in math and related areas)

See Baccalaureate Degree Requirements for general education and remaining university requirements.

Recommended Sequence of Program Requirements

FIRST YEAR
Fall�CSE 113 or CSE 115; MTH 141
Spring�CSE 114 or CSE 116; MTH 142

SECOND YEAR
Fall�MTH 241, MTH 191/CSE 191
Spring�LAI 350, MTH 311, MTH 306

THIRD YEAR
Fall�MTH 309, MTH 431
Spring�CEP 400, ELP 405, MTH 335

FOURTH YEAR
Fall�LAI 414, MTH 411, MTH 419
Spring�One 300/400-level mathematics elective (not MTH 417); two 300/400-level electives from the Educational Leadership and Policy or Counseling, School, and Educational Psychology departments, or one education-related College of Arts and Sciences course

Mathematics - B.A./M.A.

About the Program

This program is designed for students who demonstrate, in their first two years of mathematical study, a high level of competence and motivation. Upon admission to the BA/MA program, students follow an integrated course of study leading to a combined degree. Admission to this program is by departmental approval only and requires a minimum GPA of 3.0 in mathematics courses (calculus, differential equations, linear algebra) as well as letters of recommendation.

Acceptance Criteria

A minimum GPA of 2.5 in the prerequisite courses.

Prerequisite Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
MTH 241 College Calculus III

Required Courses

MTH 306 Introduction to Differential Equations
MTH 309 Introductory Linear Algebra
MTH 311 Introduction to Higher Mathematics
MTH 519 Introduction to Algebra I
MTH 520 Introduction to Algebra II
MTH 531 Introduction to Real Variables I
MTH 532 Introduction to Real Variables II
Three 300/400-level courses in mathematics or computer science. At least one of these must be a mathematics course other than MTH 417. Electives require approval by the director of undergraduate studies.
Six graduate-level courses, including at least 12 credits in mathematics. Included must be at least one year-long sequence in mathematics at the 500 level or above (other than 519-520 or 531-532). Electives require approval by the director of graduate studies.

Summary
Total required credit hours for the undergraduate portion: 33-36
Total required credit hours for the B.A./M.A.: 63-66

See Baccalaureate Degree Requirements for general education and remaining university requirements.

Refer to the Graduate School's Policies and Procedures Manual for Master's Candidate Requirements.

Recommended Sequence of Program Requirements

FIRST YEAR
Fall�MTH 141
Spring�MTH 142

SECOND YEAR
Fall�MTH 241, MTH 309
Spring�MTH 306, MTH 311

THIRD YEAR
Fall and Spring�Three 300/400-level courses in mathematics or computer science. At least one of these must be a mathematics course other than MTH 417. Electives require approval by the director of undergraduate studies in mathematics.

FOURTH YEAR
Fall�MTH 519, MTH 531
Spring�MTH 520, MTH 532

FIFTH YEAR
Fall and Spring�Six graduate-level math electives, including at least 12 credits in mathematics. Included must be at least one year-long sequence in mathematics at the 500 level or above (other than MTH 519-MTH 520 or MTH 531-MTH 532). Electives require approval by the director of graduate studies.

Project or thesis (up to 6 credits of the 18 credits of graduate level electives may be used for MTH 800 Thesis Guidance.)

Mathematics - Minor

Acceptance Criteria

Minimum GPA of 2.5 in the prerequisite courses (or approved transfer equivalent).

Prerequisite Courses

MTH 141 College Calculus I
MTH 142 College Calculus II
MTH 241 College Calculus III

Required Courses

MTH 306 Introduction to Differential Equations
MTH 309 Introductory Linear Algebra
Two additional 300/400-level mathematics electives from within the Department of Mathematics

Note: A minimum GPA of 2.0 is required in these courses for departmental recommendation for a minor in mathematics.

Summary
Total required credit hours for the minor: 26-28
(7 courses from within the Mathematics department)

Course Descriptions

MTH 115 Survey of Algebra and Trigonometry

Credits:  4
Semester: F Sp
Prerequisites:  None
Corequisites:  None
Type:  LEC/LAB

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A pre-calculus course; covers topics from the NYS Regents Course III: order, absolute value, inequalities, exponents, radicals, polynomials, rational expressions, solving systems of linear equations, quadratic equations and inequalities, functions (rational, logarithmic, exponential, trigonometric), graphing, trigonometric identities. Emphasizes applications to problems. This fast-paced course reviews Course III and prepares students for further courses in mathematics. Students with three years of high school math but with weak algebra skills should take ULC 147 before MTH 115. Students who have had only two years of high school mathematics may take MTH 115, or may prefer to take a two-semester sequence covering this material more thoroughly and at a more moderate pace: ULC 147 and ULC 148.

MTH 117 Applications of Mathematical Concepts

Credits:  3
Semester:
Prerequisites:  two years of NYS Regents-level high school mathematics
Corequisites:  None
Type:  LEC/REC

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Intended to be non-technical. Emphasizes conceptually sophisticated and aesthetically appealing mathematical discoveries of the twentieth century, such as mathematical aspects of social choice, management science, and growth and symmetry.

MTH 119 Survey of Finite Mathematics

Credits:  4
Semester:
Prerequisites:  three years of NYS Regents-level high school mathematics
Corequisites:  None
Type:  LEC/LAB

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Elementary topics in topology, probability, numerical sequences, and groups.

MTH 120 Selected Topics in Calculus

Credits:  1
Semester: F Sp
Prerequisites:  None
Corequisites:  None
Type:  TUT

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Allows transfer students to efficiently learn specific topics from UB calculus courses that were not covered in calculus courses they took at other institutions.

MTH 121 Survey of Calculus and its Applications I

Credits:  4
Semester: F Sp
Prerequisites:  NYS Regents Course III or MTH 115 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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For students in social, biological, and management sciences. Limits, continuity, differentiation of algebraic and exponential functions; applications; introduces integration.

MTH 122 Survey of Calculus and Its Applications II

Credits:  4
Semester: F Sp
Prerequisites:  MTH 121 or MTH 131 with recommended grade of C or higher
Corequisites:  None
Type:  LEC/LAB

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Continuation of MTH 121. Maximization of functions of several variables using both calculus and elementary linear programming techniques. Elementary integration, simple differential equations, matrix algebra.

MTH 131 Mathematical Analysis for Management

Credits:  4
Semester: F Sp
Prerequisites:  NYS Regents Course III or MTH 115 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB/REC

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For students in Management. Limits, continuity, differentiation of algebraic and exponential functions. Applications, partial derivatives and applications. Introduces integration.

MTH 141 College Calculus I

Credits:  4
Semester: F Sp
Prerequisites:  trigonometry or NYS Regents Course III or MTH 115 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Beginning of a three-semester sequence in calculus for students of mathematics, natural sciences, and engineering. Covers differentiation and integration with applications.

MTH 142 College Calculus II

Credits:  4
Semester: F Sp
Prerequisites:  MTH 141 with recommended grade of C or higher
Corequisites:  None
Type:  LEC/LAB

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MTH 121 is usually not adequate preparation for MTH 142.

Differentiation and integration of transcendental functions; infinite sequences; series and power series; integration methods; additional topics in analytic geometry.

MTH 153 Honors Calculus I

Credits:  4
Semester: F
Prerequisites:  permission of instructor or a score of 4 or 5 on the advanced placement calculus exam or equivalent. Credit may be given in addition to advanced placement credit
Corequisites:  None
Type:  LEC/LAB

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First course in the honors sequence for intended math majors or for others with suitable preparation. Emphasizes proofs and concepts of calculus.

MTH 154 Honors Calculus II

Credits:  4
Semester: Sp
Prerequisites:  MTH 153 with grade of C or higher recommended or permission of instructor
Corequisites:  None
Type:  LEC/LAB

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Continuation of MTH 153. May be taken in addition to advanced placement credit.

MTH 172 Principles of Mathematical Computing

Credits:  4
Semester: Sp
Prerequisites:  CSE 113 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Programming through data structures (sorting algorithms) and applications in scientific computing. Credit is not given for both MTH 172 and CSE 114.

MTH 181 Conceptual Mathematics I

Credits:  3
Semester:
Prerequisites:  high school algebra
Corequisites:  None
Type:  LEC/LAB

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Intended primarily for students not contemplating a major in the natural sciences. Concentrates on the conceptual nature of mathematics, and aids in understanding science as part of the general culture, as well as in learning to analyze and reason more clearly. Differs substantially from other beginning courses, which must emphasize the computational facility needed for advanced work. Topics include categories; adding and multiplying numbers, objects, and propositions; transformations of space and quantity.

MTH 191 Introduction to Discrete Mathematics I

Credits:  4
Semester:
Prerequisites:  working knowledge of a programming language
Corequisites:  None
Type:  LEC/LAB

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First part of a two-semester sequence. Provides the mathematical foundations for the study of computer science. Also approved for mathematics majors in Concentration GS/ED. Topics include sets, relations, functions, mathematical induction, fundamental counting methods, difference equations, and sequences and series. Same as CSE 191.

MTH 192 Introduction to Discrete Mathematics II

Credits:  4
Semester: Sp
Prerequisites:  MTH 191 or CSE 191 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Second part of a two-semester sequence. Provides the mathematical foundations for the study of computer science. Topics include discrete probability, mathematical logic, linear algebra, and graph theory. Same as CSE 192.

MTH 241 College Calculus III

Credits:  4
Semester: F Sp
Prerequisites:  MTH 142 with recommended grade of C or higher
Corequisites:  None
Type:  LEC/LAB

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MTH 121-MTH 122 is usually not adequate preparation for MTH 241.

Geometry and vectors of n-dimensional space; Green's theorem, Gauss theorem, Stokes theorem; multidimensional differentiation and integration; application to 2- and 3-D space.

MTH 251 Honors Calculus III

Credits:  4
Semester: F
Prerequisites:  permission of instructor
Corequisites:  None
Type:  LEC/LAB

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Third-semester calculus course for honors students and students with an excellent record in previous calculus courses. Emphasizes proofs and concepts of calculus.

MTH 272 Mathematics of Data Manipulation

Credits:  4
Semester: Sp
Prerequisites:  MTH 172 or CSE 114 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Aspects of data representation and manipulation needed for applications programming together with an introduction to their mathematical theory.

MTH 306 Introduction to Differential Equations

Credits:  4
Semester: F Sp
Prerequisites:  MTH 142 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Analytic solutions, qualitative behavior of solutions to differential equations. First-order and higher-order ordinary differential equations, including nonlinear equations. Covers analytic, geometric, and numerical perspectives as well as an interplay between methods and model problems. Discusses necessary matrix theory and explores differential equation models of phenomena from various disciplines. Uses a mathematical software system designed to aid in the numerical and qualitative study of solutions, and in the geometric interpretation of solutions.

MTH 309 Introductory Linear Algebra

Credits:  4
Semester: F Sp
Prerequisites:  MTH 142 or MTH 192 or CSE 192 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Linear equations, matrices, determinants, vector spaces, linear mappings, inner products, eigenvalues, eigenvectors.

MTH 310 Applications of Linear Algebra

Credits:  4
Semester: F Sp
Prerequisites:  MTH 306, MTH 309 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Topics selected by the instructor.

MTH 311 Introduction to Higher Mathematics

Credits:  4
Semester: F Sp
Prerequisites:  MTH 241 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Develops the student's ability to read, comprehend and construct rigorous proofs. Topics may include the following: the number systems N, Z, Q, R and the existence of irrational numbers; sets and functions; size of sets (finite/infinite, countable/uncountable); the countability of the rationals and the uncountability of the real numbers; boundedness; upper and lower bounds; lub's and glb's; lub and glb property; density of the rationals in the reals; Archimedean property of the reals; mathematical induction, including strong induction and the well-ordering of the natural numbers; sequences of real numbers, including the Monotone Convergence Theorem, Cauchy sequences, and the Bolzano-Weierstrass Theorem.

MTH 313 Elements of Set Theory

Credits:  4
Semester:
Prerequisites:  MTH 241 with grade of C or higher recommended or permission of instructor
Corequisites:  None
Type:  LEC/REC

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Cardinals, ordinals, order-types, and operations on them. Axiom of choice. Sets.

MTH 314 Logic for Computer Science

Credits:  3
Semester: F
Prerequisites:  at least one year of previous training in college mathematics and one year of programming
Corequisites:  None
Type:  LEC

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Introduces predicate calculus, emphasizing proof theory rather than model theory. Gives some programming exercises.

MTH 335 Elements of Geometry

Credits:  4
Semester: Sp
Prerequisites:  MTH 311, MTH 309 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Euclidean and non-Euclidean geometries. Studies the Hilbert postulates and various models, emphasizing Euclidean and Lobachevskian geometries.

MTH 336 Projective Geometry

Credits:  4
Semester:
Prerequisites:  MTH 241 with grade of C or higher recommended or permission of instructor
Corequisites:  None
Type:  LEC

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Projective geometry is both a generalization and a simplification of familiar Euclidean geometry, omitting concepts of distance and angle. The small set of axioms has an important duality property. There are several famous theorems relating figures in the plane. May consider Three-D geometry and specialization to Euclidean and other geometries, as time permits. Requires no previous geometry.

MTH 337 Introduction to Scientific Computing

Credits:  4
Semester: F Sp
Prerequisites:  MTH 141 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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For students in all scientific disciplines. Introduces the fundamental numerical techniques used in high-performance scientific computing, including sorting, numerical integration, root finding for nonlinear systems, elementary linear algebra, and basic ordinary differential equations. Emphasizes an experimental approach to scientific computing. Students learn the basics of UNIX, write and debug programs in FORTRAN, and use computational and visualization tools in Matlab. Cross-listed as CSE 337.

MTH 343 Codes

Credits:  3
Semester:
Prerequisites:  MTH 309 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Studies the characteristics and mathematical foundations of several codes widely used in information handling for data compression, error detection, error correction and other special purposes. The codes studied include binary, comma-free, cryptographic, cyclic, Hamming, and Huffman.

MTH 353 Introduction to Combinatorics I

Credits:  3
Semester: F
Prerequisites:  MTH 241 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Permutations, combinations, and other problems of selecting and arranging objects subject to various restrictions; generating functions; recurrence relations; inclusion-exclusion theorem.

MTH 354 Introduction to Combinatorics II

Credits:  3
Semester: Sp
Prerequisites:  MTH 241 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Theory of graphs: Eulerian and Hamiltonian circuits; trees; planarity; colorability; directed graphs and tournaments; isomorphism; adjacency matrix; applications to problems in communication, scheduling, and traffic flow.

MTH 411 Probability Theory

Credits:  4
Semester: F Sp
Prerequisites:  MTH 141-MTH 142 or equivalent with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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A first course in probability. Introduces the basic concepts of probability theory and addresses many concrete problems. A list of basic concepts includes axioms of probability, conditional probability, independence, random variables (continuous and discrete), distribution functions, expectation, variance, joint distribution functions, limit theorems.

MTH 412 Introduction to Statistical Inference

Credits:  4
Semester: Sp
Prerequisites:  MTH 141 or equivalent and MTH 411 or STA 401 with grade of C or higher recommended, or permission of instructor
Corequisites:  None
Type:  LEC/LAB

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Topics include: review of probability, conditional probability, Bayes' Theorem; random variables and distributions; expectation and properties; covariance, correlation, and conditional expectation; special distributions; Central Limit Theorem and applications; estimations, including Bayes; estimators, maximum likelihood estimators, and their properties. Includes use of sufficient statistics to improve estimators, distribution of estimators, unbiasedness, hypothesis testing, linear statistical models, and statistical inference from the Bayesian point of view.

MTH 413 Introduction to Mathematical Logic I

Credits:  3
Semester: F
Prerequisites:  MTH 313 with grade of C or higher recommended or permission of instructor
Corequisites:  None
Type:  LEC

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Informal and formal development of propositional calculus; predicate calculus and predicate calculus with equality; completeness theorem and some consequences.

MTH 414 Introduction to Mathematical Logic II

Credits:  3
Semester: Sp
Prerequisites:  MTH 314 or MTH 413 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Godel's incompleteness theorem; decidability and recursiveness; consistency problems.

MTH 417 Survey of Multivariable Calculus

Credits:  4
Semester: F Sp
Prerequisites:  MTH 241 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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For math majors in Concentration C, and majors of science and engineering. Surveys functions of several variables; differentiation, composite, and implicit functions; critical points; line integrals; Green's theorem. Vector field theory; gradient, divergence, and curl; integral theorems. Introduces functions of a complex variable; curves and regions in the complex plane; analytic functions, Cauchy-Riemann equations, Cauchy integral formula. Applications.

MTH 418 Survey of Partial Differential Equations

Credits:  4
Semester: F Sp
Prerequisites:  MTH 306 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Surveys elementary differential equations of physics; separation of variables and superposition of solutions; orthogonal functions and Fourier series. Introduces boundary value problems, Fourier and Laplace transforms.

MTH 419 Introduction to Algebra I

Credits:  4
Semester: F Sp
Prerequisites:  MTH 309; MTH 311 recommended with grade of C or higher recommended
Corequisites:  None
Type:  LEC/REC

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Topics in finite rings and algebraic number theory.

MTH 420 Introduction to Algebra II

Credits:  4
Semester: Sp
Prerequisites:  MTH 309; MTH 311 recommended with grade of C or higher recommended
Corequisites:  None
Type:  LEC/REC

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Topics in advanced linear algebra.

MTH 424 Survey of Fourier Series Methods

Credits:  3
Semester:
Prerequisites:  MTH 431 or permission of instructor
Corequisites:  None
Type:  LEC

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Theory of Fourier series and transforms, orthogonal sets, special functions, applications.

MTH 425 Introduction to Complex Variables I

Credits:  3
Semester:
Prerequisites:  MTH 417 or MTH 431 with grade of C or higher recommended or permission of instructor
Corequisites:  None
Type:  LEC

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For students of physics, electrical and other areas of engineering, and mathematics. Analyticity; calculus over the complex numbers. Cauchy theorems, residues, singularities, conformal mapping. Weierstrass convergence theorem; analytic continuation.

MTH 426 Introduction to Complex Variables II

Credits:  3
Semester:
Prerequisites:  MTH 425 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Continuation of MTH 425. Weierstrass and Mittag-Leffler theorems, harmonic functions, conformal mapping and Green's function, analytic equivalence, and Riemann's mapping theorem. Montel's theorem, external mappings.

MTH 427 Introduction to Topology I

Credits:  3
Semester: F
Prerequisites:  MTH 431with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Abstract topological spaces, bases, convergence, filters, and nets; separation axioms, continuity, and homeomorphisms; connectedness, separability, compactness.

MTH 428 Introduction to Topology II

Credits:  3
Semester: Sp
Prerequisites:  MTH 427 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Continuation of MTH 427. Product and quotient topologies; compactification; complete semi-metric spaces; metrization; topological algebra. Applies results to such fields as differential equations, numerical analysis, probability theory.

MTH 429 Introduction to the Theory of Numbers I

Credits:  3
Semester: F
Prerequisites:  MTH 419 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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The Euclidean algorithm and unique factorization; arithmetical functions; congruences, reduced residue systems; primitive roots; certain diophantine equations.

MTH 430 Introduction to the Theory of Numbers II

Credits:  3
Semester: Sp
Prerequisites:  MTH 429 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Continuation of MTH 429. Irrational numbers; continued fractions from a geometric viewpoint; best rational approximations to real numbers; the Fermat-Pell equation; quadratic fields and integers. Applications to diophantine equations.

MTH 431 Introduction to Real Variables I

Credits:  4
Semester: F Sp
Prerequisites:  MTH 311 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Comprehensive and rigorous course in the study of real valued functions of one real variable. Topics include sequences of numbers, limits and the Cauchy criterion, continuous functions, differentiation, inverse function theorem, Riemann integration, sequences and series, uniform convergence. A prerequisite for most advanced courses in analysis.

MTH 432 Introduction to Real Variables II

Credits:  4
Semester: Sp
Prerequisites:  MTH 431with grade of C or higher recommended
Corequisites:  None
Type:  LEC/REC

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Rigorous course in analyzing dimensions greater than one. Includes details of three basic theorems: the inverse function theorem, the implicit function theorem, and the change of variables theorem in multiple integrals. Topics include continuously differentiable functions, the chain rule, inverse and implicit function theorems, Riemann integration, partitions of unity, change of variables theorem.

MTH 434 Basic Measure Theory

Credits:  3
Semester:
Prerequisites:  MTH 431 with grade of C or higher recommended or permission of instructor
Corequisites:  None
Type:  LEC/LAB

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The real numbers, the extended numbers, sequences, limit superior and limit inferior, topology for the real numbers and continuity of functions. The Lebesgue outer measure, measurable sets and Lebesgue measure, nonmeasurable sets, measurable functions. Egoroff's Theorem and Lusin's Theorem. The Riemann integral, the Lebesgue integral and the convergence theorems. Differentiation of functions of bounded variation, absolute continuity. The Lp spaces.

MTH 435 Introduction to Cryptography

Credits:  3
Semester: F
Prerequisites:  MTH 419 or MTH 429 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Explains the basics of cryptography, which is the systematic study of methods of concealing messages from people who are not authorized to read them. Topics include the following: cryptosystem definitions and basic types of attack; substitution ciphers. Hill ciphers; congruences and modular exponentiation; digital encryption standard; public key and RSA cryptosystems; pseudoprimes and primality testing; Pollard rho method; basic finite field theory; discrete log; and digital signatures.

MTH 437 Introduction to Numerical Analysis I

Credits:  4
Semester: F
Prerequisites:  CSE 113 or CSE 115; MTH 241, MTH 306, MTH 309 with grade of C or higher recommended, or permission of instructor
Corequisites:  None
Type:  LEC/LAB

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First part of a 2-semester sequence which explores the design and implementation of numerical methods to solve the most common types of problem arising in science and engineering. Most such problems cannot be solved in terms of a closed analytical formula, but many can be handled with numerical methods learned in this course. Topics for the two semesters include: how a computer does arithmetic, solving systems of simultaneous linear or nonlinear equations, finding eigenvalues and eigenvectors of (large) matrices, minimizing a function of many variables, fitting smooth functions to data points (interpolation and regression), computing integrals, solving ordinary differential equations (initial and boundary value problems), and solving partial differential equations of elliptic, parabolic, and hyperbolic types. We study how and why numerical methods work, and also their errors and limitations. Students gain practical experience through course projects that entail writing computer programs.

MTH 438 Introduction to Numerical Analysis II

Credits:  4
Semester: Sp
Prerequisites:  MTH 437 or CSE 437 with grade of C or higher recommended
Corequisites:  None
Type:  LEC/LAB

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Second part of the 2-semester sequence described under MTH 437.

MTH 443 Fundamentals of Applied Mathematics I

Credits:  4
Semester:
Prerequisites:  MTH 306 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Mathematical formulation and analysis of models for phenomena in the natural sciences. Includes derivation of relevant differential equations from conservation laws and constitutive relations. Potential topics include diffusion, stationary solutions, traveling waves, linear stability analysis, scaling and dimensional analysis, perturbation methods, variational and phase-space methods, kinematics, and laws of motion for continuous media. Examples from areas might include, but are not confined to, biology, fluid dynamics, elasticity, chemistry, astrophysics, geophysics.

MTH 444 Fundamentals of Applied Mathematics II

Credits:  4
Semester:
Prerequisites:  MTH 306 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Explores other topics described in MTH 443.

MTH 445 Ordinary Differential Equations

Credits:  3
Semester:
Prerequisites:  MTH 431 with grade of C or higher recommended or permission of instructor
Corequisites:  None
Type:  LEC

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For students with a strong mathematics background. Existence and uniqueness of solutions; continuation of solutions; dependence on initial conditions and parameters; linear systems of equations with constant and variable coefficients; autonomous systems, phase space, and stability.

MTH 449 Introduction to Partial Differential Equations

Credits:  3
Semester:
Prerequisites:  permission of instructor
Corequisites:  None
Type:  LEC

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For students with a strong mathematics background. Students must know the material of both MTH 431 and MTH 306. Classical linear equations of mathematical physics, well-posed problems, solutions' qualitative properties. Techniques for solving problems.

MTH 451 Design Process and Methods

Credits:  3
Semester:
Prerequisites:  None
Corequisites:  None
Type:  LEC

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Discusses the fundamental concepts and activities of design processes. Investigates domain-independent topics of design processes. These topics include idea conception, teamwork, quality, experimental design, optimization, and technical communication. In addition, discusses fundamental methods of design, including decision making, conceptual design, cost evaluation, ethics issues, and intellectual property issues, which are investigated through interactive lectures and individual and group exercises.

MTH 455 Mathematical Modeling

Credits:  3
Semester:
Prerequisites:  MTH 306, MTH 309 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Introduces the use of mathematical modeling in applied mathematics using a case study approach. Population ecology; chemical kinetics; traffic dynamics.

MTH 456 The Mathematics of Voting

Credits:  3
Semester: Sp
Prerequisites:  Junior or senior standing
Corequisites:  None
Type:  LEC

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Introduces the mathematical theory of voting - the systemic analysis of the ways to determine a choice of a group from the choices of individuals within a group - with applications to economics and politics. Examines voting procedures including the standard plurality vote, the antiplurality vote, the Borda count, Condorcets's method, and run-off elections. Provides an understanding of how different procedures effect group decisions. Uses convex geometry in the plane and in three spaces. Also discusses political power.

MTH 457 Problem Solving Seminar

Credits:  3
Semester:
Prerequisites:  MTH 306, MTH 411 or STA 401, and some experience with specific programming; minimum grade of B in these courses
Corequisites:  None
Type:  LEC

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Open discussion and solving of a series of quantitatively based problems involving both individual and student team efforts. Central to the active and cooperative learning experience is communicating results via carefully written technical reports and oral presentations. Analytic, geometric, and numerical problem solving techniques may all be used.

MTH 458 Mathematical Finance

Credits:  3
Semester:
Prerequisites:  MTH 241, MTH 306, MTH 309 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Introduces the mathematical theory and computation of modern financial products used in the banking and corporate world. Derives and analyzes mathematical models for the valuation of derivative products.

MTH 459 Mathematical Finance 2

Credits:  3
Semester:
Prerequisites:  MTH 458 with grade of C or higher recommended
Corequisites:  None
Type:  LEC

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Describes the mathematical development of both the theoretical and the computational techniques used to analyze financial instruments. Specific topics include utility functions; forwards, futures, and swaps; and modeling of derivatives and rigorous mathematical analysis of the models, both theoretically and computationally. Develops, as needed, the required ideas from partial differential equations and numerical analysis.

MTH 460 Theory of Games

Credits:  4
Semester:
Prerequisites:  MTH 241, MTH 309 with grade of C or higher recommended, or permission of instructor
Corequisites:  None
Type:  LEC/LAB

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Introduces the mathematical theory of games--a systematic approach to modeling conflict, competition, cooperation, and negotiation--with applications to mathematics, economics, politics and evolutionary biology. A game, in mathematical terms, consists of a starting point and various choices made by 'players.' Each choice might lead to new choices or to an outcome that ends the game. Some choices might be random; some might be made without full information about what has transpired. The players are each trying to maximize their own payoff, but the play of each might influence the results of the others. The approaches Game Theory uses to analyze conflict between two or more people lead to results that can seem paradoxical as well as illuminating. The most important thing a student can take from this course is a useful way of approaching decisions, from the trivial-- how does a couple decide which movie to see--to the critical--how should countries pursue their goals in cooperation or conflict with their allies and enemies. Partial list of topics: Prisoner's Dilemma, game trees, pure and mixed strategies, backward induction, normal form, Nash equilibrium, chance moves, utility functions, domination, convexity, payoff regions, strictly competitive games, separating hyperplanes, repeating games, and cooperative bargaining theory.

MTH 461 Topics in Algebra

Credits:  3
Semester:
Prerequisites:  permission of instructor
Corequisites:  None
Type:  LEC

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The content of this course is variable and therefore it is repeatable for credit. The University Grade Repeat Policy does not apply.

Treats problems, methods, and recent developments pertaining to a specific area of algebra. Topics courses can be taken more than once for credit.

MTH 462 Topics in Analysis

Credits:  3
Semester:
Prerequisites:  permission of instructor
Corequisites:  None
Type:  LEC

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The content of this course is variable and therefore it is repeatable for credit. The University Grade Repeat Policy does not apply.

Treats problems, methods, and recent developments pertaining to analysis. Topics courses can be taken more than once for credit.

MTH 463 Topics in Applied Mathematics

Credits:  3
Semester:
Prerequisites:  permission of instructor
Corequisites:  None
Type:  LEC

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The content of this course is variable and therefore it is repeatable for credit. The University Grade Repeat Policy does not apply.

Treats problems, methods, and recent developments pertaining applied mathematics. Topics courses can be taken more than once for credit.

MTH 464 Topics in Combinatorial Analysis

Credits:  3
Semester:
Prerequisites:  permission of instructor
Corequisites:  None
Type:  LEC

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The content of this course is variable and therefore it is repeatable for credit. The University Grade Repeat Policy does not apply.

Treats problems, methods, and recent developments pertaining combinatorial analysis. Topics courses can be taken more than once for credit.

MTH 465 Lectures in Geometry

Credits:  3
Semester:
Prerequisites:  permission of instructor
Corequisites:  None
Type:  LEC

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The content of this course is variable and therefore it is repeatable for credit. The University Grade Repeat Policy does not apply.

Provides a broader understanding of differential geometry. Comprehensively introduces the theory of curves and surfaces in space. Moves toward the goal of viewing surfaces as special concrete examples of differentiable manifolds, reached by studying surfaces using tools that are basic to studying manifolds. Topics include curves in 3-D space, differential forms, Frenet formulae, patch computations, curvature, isometries, intrinsic geometry of surfaces. Serves as an introduction to more advanced courses involving differentiable manifolds.

MTH 466 Topics in Logic and Set Theory

Credits:  3
Semester:
Prerequisites:  permission of instructor
Corequisites:  None
Type:  LEC

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The content of this course is variable and therefore it is repeatable for credit. The University Grade Repeat Policy does not apply.

Treats problems, methods, and recent developments pertaining logic and set theory. Topics courses can be taken more than once for credit.

MTH 467 Topics in Number Theory

Credits:  3
Semester:
Prerequisites:  permission of instructor
Corequisites:  None
Type:  LEC

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The content of this course is variable and therefore it is repeatable for credit. The University Grade Repeat Policy does not apply.

Treats problems, methods, and recent developments pertaining number theory. Topics courses can be taken more than once for credit.

MTH 468 Topics in Numerical Analysis

Credits:  3
Semester:
Prerequisites:  permission of instructor
Corequisites:  None
Type:  LEC

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The content of this course is variable and therefore it is repeatable for credit. The University Grade Repeat Policy does not apply.

Treats problems, methods, and recent developments pertaining numerical analysis. Topics courses can be taken more than once for credit.

MTH 469 Topics in Topology

Credits:  3
Semester:
Prerequisites:  permission of instructor
Corequisites:  None
Type:  LEC

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The content of this course is variable and therefore it is repeatable for credit. The University Grade Repeat Policy does not apply.

Treats problems, methods, and recent developments pertaining topology. Topics courses can be taken more than once for credit.

MTH 470 Topics in Mathematics

Credits:  3
Semester:
Prerequisites:  variable ( set by instructor)
Corequisites:  None
Type:  LEC

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Treats problems, methods, and recent developments in any area of mathematics that does not fit nearly or fully under the title of any other "Topics in..." course.

MTH 496 Internship in Mathematics

Credits:  1 - 4
Semester: F Sp
Prerequisites:  Accepted math major, junior/senior standing with a minimum of 24 credits in mathematics, permission of director of undergraduate studies
Corequisites:  None
Type:  TUT

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Students get field experience in mathematical employment,in business, industry or education, working under the joint supervision of an off-campus supervisor and a university faculty member, usually the director of undergraduate studies. May be taken once only.

MTH 497 Honors Thesis in Mathematics

Credits:  4
Semester: F Sp
Prerequisites:  math major seeking honors degree in mathematics
Corequisites:  None
Type:  TUT

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The content of this course is variable and therefore it is repeatable for credit. The University Grade Repeat Policy does not apply.

Open only to math majors intending to seek an honors degree in mathematics. For information, consult the director of undergraduate studies in the Department of Mathematics.

MTH 499 Independent Study

Credits:  1 - 4
Semester: F Sp
Prerequisites:  None
Corequisites:  None
Type:  TUT

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The content of this course is variable and therefore it is repeatable for credit. The University Grade Repeat Policy does not apply.

Individual study arranged between student and faculty member in an area of mathematics of particular interest to the student.

 

Updated: Apr 12, 2006 11:04:31 AM