- Mathematics - B.S. (Concentration BSc: General Study in Mathematics)
- Mathematics - B.S. (Concentration BSc/AM: General Study in Applied Mathematics)
- Mathematical Physics - B.S.
- Mathematics - B.A. (General Curriculum in Mathematics)
- Mathematics - B.A. (Concentration C: Computing and Applied Mathematics)
- Mathematics - B.A. (Concentration GS: General Study in Mathematics)
- Mathematics - B.A. (Concentration GS/AM: General Study in Applied Mathematics)
- Mathematics - Economics - B.A. (Program M/E: Joint Major in Mathematics/Economics)
- Mathematics - B.A. (Concentration GS/ED: General Study in Mathematics and Education)
- Mathematics - B.A./M.A.
- Mathematics - Minor
- Course Descriptions
- Undergraduate Faculty Listings

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

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.

**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.

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.*

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.

**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 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.

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.

Minimum GPA of 2.5 in the prerequisite courses.

MTH 141 College Calculus I

MTH 142 College Calculus II

MTH 241 College Calculus III

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.**

**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.*

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.

Minimum GPA of 2.5 in the prerequisite courses.

MTH 141 College Calculus I

MTH 142 College Calculus II

MTH 241 College Calculus III

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.**

**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.*

Minimum GPA of 2.5 in the prerequisite courses.

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.

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

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.**

**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

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.

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

MTH 141 College Calculus I

MTH 142 College Calculus II

MTH 241 College Calculus III

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.**

**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*

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.

Minimum GPA of 2.5 in the prerequisite courses.

MTH 141 College Calculus I

MTH 142 College Calculus II

MTH 241 College Calculus III

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.**

**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.*

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

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.

Minimum GPA of 2.5 in the prerequisite courses.

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.

MTH 141 College Calculus I

MTH 142 College Calculus II

MTH 241 College Calculus III

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.**

**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)

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.

A minimum GPA of 2.5 in the prerequisite courses.

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.

MTH 141 College Calculus I

MTH 142 College Calculus II

MTH 241 College Calculus III

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.**

**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)

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.

A minimum GPA of 2.5 in the prerequisite courses.

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.

MTH 141 College Calculus I

MTH 142 College Calculus II

MTH 241 College Calculus III

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.**

**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)

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.

A minimum GPA of 2.5 in the prerequisite courses.

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.

MTH 141 College Calculus I

MTH 142 College Calculus II

MTH 241 College Calculus III

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.**

**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

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.

A minimum GPA of 2.5 in the prerequisite courses.

MTH 141 College Calculus I

MTH 142 College Calculus II

MTH 241 College Calculus III

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.**

**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.)

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

MTH 141 College Calculus I

MTH 142 College Calculus II

MTH 241 College Calculus III

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)*

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

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

View Schedule*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.

**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.

**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.

**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.

**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.

**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.

**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.

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

View Schedule*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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

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

View Schedule*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.

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

View Schedule*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.

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

View Schedule*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.

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

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

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

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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.

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

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

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

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

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

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

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

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

**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.

**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.

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

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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.

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

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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