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*Keith Promislow, Chairperson *

The department packages its courses into flexible programs that can adapt to many different career paths. Students with an interest in mathematics are encouraged, regardless of their preferred major, to contact the Department of Mathematics prior to registration to discuss course options. Students may benefit from advanced placement, participation in Honors courses designed to prepare motivated students for graduate study, or from pursuit of a degree in Actuarial Science.

The Department of Mathematics offers degree opportunities leading to a Bachelor of Arts or a Bachelor of Science in Mathematics, a Bachelor of Arts or a Bachelor of Science, Mathematics, Advanced, a Bachelor of Science in Computational Mathematics, and a Bachelor of Science in Actuarial Science. The Bachelor of Arts degree programs require a higher level of foreign language competency, while the Bachelor of Science degree programs require science proficiency beyond that established by the college.

Graduates with the Bachelor of Art and Bachelor of Science degrees find a wide range of career options in industry and teaching fields. The Bachelor of Arts and Bachelor of Science programs prepare students for continuing study in top graduate schools or for the pursuit of careers in mathematically intensive fields. The Bachelor of Science in Computational Mathematics prepares students for either for graduate study or for careers that rely upon computational models and tools.

Students with a Bachelor of Science degree in Actuarial Science are sought after by insurance companies, banks, investment firms, government agencies, and businesses that weigh the financial consequences of risk. Course work prepares students for the Society of Actuaries examinations as well as the Validation by Educational Experience course work necessary to become an Associate of the Society of Actuaries.

A Minor in Mathematics and a Minor in Actuarial Science are also available.

**Admission to the Major**

To be considered for admission to the major, the student must have:

- a cumulative grade-point average of at least 3.0 in all courses taken at MSU.
- a minimum average grade of 3.0 in MTH 132, MTH 133, and MTH 234 or equivalent for transfer students.
- a minimum average of 3.0 in the grades in MTH 360 and STT 441.

Students who declare the major in actuarial science are automatically reviewed at the end of every semester and are either admitted or informed of their progress. Students must be admitted to a degree-granting college at the time they have completed 56 credits. Those who do not meet the criteria may consider a major in either Mathematics or in Statistics and Probability.**Requirements for the Bachelor of Science Degree in Actuarial Science**

- The University requirements for bachelor’s degrees as described in the
*Undergraduate Education*section of this catalog; 120 credits, including general elective credits, are required for the Bachelor of Science degree in Actuarial Science.

The University’s Tier II writing requirement for the Actuarial Science major is met by completing Mathematics 309 or 496. Those courses are referenced in item 3. below.

Students who are enrolled in the College of Natural Science may complete the alternative track to Integrative Studies in Biological and Physical Sciences that is described in item 1. under the heading Graduation Requirements in the College statement. Certain courses referenced in requirement 3. below may be used to satisfy the alternative track. - The requirements of the College of Natural Science for the Bachelor of Science degree.

The credits earned in certain courses referenced in requirement 3. below may be counted toward College requirements as appropriate. - The following requirements for the major:

a. | One course of at least 3 credits in biological science, entomology, microbiology, physiology, plant biology, or integrative biology. | |||||||

b. | One of the following groups of courses (8 or 10 credits): | |||||||

(1) | CEM | 141 | General Chemistry | 4 | ||||

CEM | 142 | General and Inorganic Chemistry | 3 | |||||

CEM | 161 | Chemistry Laboratory I | 1 | |||||

(2) | CEM | 151 | General and Descriptive Chemistry | 4 | ||||

CEM | 152 | Principles of Chemistry | 3 | |||||

CEM | 161 | Chemistry Laboratory I | 1 | |||||

(3) | CEM | 181H | Honors Chemistry I | 4 | ||||

CEM | 182H | Honors Chemistry II | 4 | |||||

CEM | 185H | Honors Chemistry Laboratory I | 2 | |||||

(4) | LB | 171 | Principles of Chemistry I | 4 | ||||

LB | 171L | Introductory Chemistry Laboratory I | 1 | |||||

LB | 172 | Principles of Chemistry II | 3 | |||||

c. | One of the following groups of courses (8 credits): | |||||||

(1) | PHY | 183 | Physics for Scientists and Engineers I | 4 | ||||

PHY | 184 | Physics for Scientists and Engineers II | 4 | |||||

(2) | PHY | 193H | Honors Physics I – Mechanics | 4 | ||||

PHY | 294H | Honors Physics II – Electromagnetism | 4 | |||||

(3) | LB | 273 | Physics I | 4 | ||||

LB | 274 | Physics II | 4 | |||||

d. | One of the following groups of courses (6 to 8 credits): | |||||||

(1) | MTH | 132 | Calculus I | 3 | ||||

MTH | 133 | Calculus II | 4 | |||||

(2) | LB | 118 | Calculus I | 4 | ||||

LB | 119 | Calculus II | 4 | |||||

(3) | MTH | 152H | Honors Calculus I | 3 | ||||

MTH | 153H | Honors Calculus II | 4 | |||||

e. | One of the following courses (4 credits): | |||||||

LB | 220 | Calculus III | 4 | |||||

MTH | 234 | Multivariable Calculus | 4 | |||||

MTH | 254H | Honors Multivariable Calculus | 4 | |||||

f. | One of the following courses (3 credits): | |||||||

MTH | 235 | Differential Equations | 3 | |||||

MTH | 340 | Ordinary Differential Equations I | 3 | |||||

g. | One of the following courses (1 credit): | |||||||

MTH | 490 | Directed Studies | 1 | |||||

MTH | 491B | Teamwork Experience | 1 | |||||

h. | All of the following courses ( 24 credits): | |||||||

MTH | 309 | Linear Algebra I | 3 | |||||

MTH | 360 | Theory of Mathematical Interest | 3 | |||||

MTH | 361 | Financial Mathematics for Actuaries I | 3 | |||||

MTH | 458 | Financial Mathematics for Actuaries II | 3 | |||||

STT | 441 | Probability and Statistics I: Probability | 3 | |||||

STT | 455 | Actuarial Models I | 3 | |||||

STT | 456 | Actuarial Models II | 3 | |||||

STT | 459 | Construction and Evaluation of Actuarial Models | 3 | |||||

i. | One of the following courses (3 credits): | |||||||

MTH | 457 | Introduction to Financial Mathematics | 3 | |||||

STT | 442 | Probability and Statistics II: Statistics | 3 | |||||

j. | One of the following courses (3 credits): | |||||||

MTH | 491A | Actuarial Internship | 3 | |||||

MTH | 496 | Capstone in Mathematics (W) | 3 | |||||

k. | All of the following courses (15 credits): | |||||||

ACC | 230 | Survey of Accounting Concepts | 3 | |||||

EC | 201 | Introduction to Microeconomics | 3 | |||||

EC | 202 | Introduction to Macroeconomics | 3 | |||||

FI | 311 | Financial Management | 3 | |||||

FI | 321 | Theory of Investments | 3 | |||||

l. | One of the following courses (3 or 4 credits): | |||||||

CSE | 131 | Technical Computing and Problem Solving | 3 | |||||

CSE | 231 | Introduction to Programming I | 4 |

**Requirements for the Bachelor of Science Degree in Computational Mathematics**

- The University requirements for bachelor's degrees as described in the
*Undergraduate Education*section of this catalog; 120 credits, including general elective credits, are required for the Bachelor of Science degree in Computational Mathematics.

The University's Tier II writing requirement for the Computational Mathematics major is met by completing Mathematics 309 or 310 and 496. Those courses are referenced in item 3. c. (1) below.

Students who are in the teacher certification program are required to complete Mathematics 330 or 432 and Statistics and Probability 430.

Students who are enrolled in the College of Natural Science may complete the alternative track to Integrative Studies in Biological and Physical Sciences that is described in item 1. under the heading Graduation Requirements in the College statement. Certain courses referenced in requirement 3. below may be used to satisfy the alternative track. - The requirements of the College of Natural Science for the Bachelor of Science degree.

The credits earned in certain courses referenced in requirement 3. below may be counted toward College requirements as appropriate. - The following requirements for the major:
a. The following courses outside the Department of Mathematics (28 or 29 credits): (1) One course of at least 3 credits in biological science, entomology, microbiology, physiology, plant biology, or integrative biology. At least 2 credits in laboratory in biological science, chemistry, entomology, microbiology, physiology, plant biology, or integrative biology. Any course noted in item (2) (c) below may count towards the 2 credit laboratory requirement. (2) One course from each of the following groups (8 or 10 credits): (a) CEM 141 General Chemistry 4 CEM 151 General and Descriptive Chemistry 4 CEM 181H Honors Chemistry I 4 LB 171 Principles of Chemistry I 4 (b) CEM 142 General and Inorganic Chemistry 3 CEM 152 Principles of Chemistry 3 CEM 182H Honors Chemistry II 4 LB 172 Principles of Chemistry II 3 (c) CEM 161 Chemistry Laboratory I 3 CEM 185H Honors Chemistry Laboratory I 2 LB 171L Introductory Chemistry Laboratory I 1 (3) Both of the following courses (8 credits): CSE 231 Introduction to Programming I 4 CSE 232 Introduction to Programming II 4 (4) One course from each of the following groups (8 credits): (a) PHY 183 Physics for Scientists and Engineers I 4 LB 273 Physics I 4 (b) PHY 184 Physics for Scientists and Engineers II 4 LB 274 Physics II 4 b. First–year competency in a foreign language or For students, who have been admitted to the teacher certification program, completion of the Professional Education Courses in the Department of Teacher Education. c. A total of 33 to 40 credits in courses in the Department of Mathematics including: (1) One course from each of the following two groups (6 to 8 credits): (a) MTH 132 Calculus I 3 MTH 152H Honors Calculus 3 LB 118 Calculus I 4 (b) MTH 133 Calculus II 4 MTH 153H Honors Calculus II 3 LB 119 Calculus II 4 (2) One of the following courses (3 or 4 credits): MTH 234 Multivariable Calculus 4 MTH 254H Honors Multivariable Calculus 3 LB 220 Calculus III 4 (3) One of the following two groups (4 or 7 credits): (a) MTH 299 Transitions 4 MTH 309 Linear Algebra I 3 (b) MTH 317H Honors Linear Algebra 4 (4) One course from each of the following groups (6 credits): (a) MTH 310 Abstract Algebra I and Number Theory 3 MTH 418H Honors Algebra I 3 (b) MTH 320 Analysis I 3 MTH 327H Honors Introduction to Analysis 3 (5) All of the following courses (9 credits): MTH 451 Numerical Analysis I 3 MTH 481 Discrete Mathematics I 3 MTH 496 Capstone in Mathematics (W) 3 The completion of Mathematics 496 satisfies the capstone course requirement of the computational mathematics major. (6) One of the following courses (3 credits): MTH 452 Numerical Analysis II 3 MTH 482 Discrete Mathematics II 3 (7) One of the following courses (3 credits): MTH 235 Differential Equations 3 MTH 340 Ordinary Differential Equations I 3 MTH 347H Honors Ordinary Differential Equations 3 d. At least one of the following courses (3 credits): Students who select Mathematics 452 or 482 may count the credits toward either requirement 3.c.(6) or 3.d. but not toward both of those requirements. Approval of the Department of Computer Science and Engineering is required to enroll in Computer Science and Engineering 331 and 440. CSE 331 Algorithms and Data Structures 3 CSE 440 Introduction to Artificial Intelligence 3 MTH 360 Theory of Mathematical Interest 3 MTH 415 Applied Linear Algebra 3 MTH 416 Introduction to Algebraic Coding 3 MTH 441 Ordinary Differential Equations II 3 MTH 452 Numerical Analysis II 3 MTH 457 Introduction to Financial Mathematics 3 MTH 482 Discrete Mathematics II 3 STT 351 Probability and Statistics for Engineering 3 STT 430 Introduction to Probability and Statistics 3 STT 441 Probability and Statistics I: Probability 3 STT 455 Actuarial Models I 3 STT 461 Computations in Probability and Statistics 3

**Requirements for the Bachelor of Arts Degree in Computational Mathematics**

- The University requirements for bachelor's degrees as described in the
*Undergraduate Education*section of this catalog; 120 credits, including general elective credits, are required for the Bachelor of Arts degree in Computational Mathematics.

The University's Tier II writing requirement for the Computational Mathematics major is met by completing Mathematics 309 or 310 and 496. Those courses are referenced in item 3.c.(1) below.

Students who are in the teacher certification program are required to complete Mathematics 330 or 432 and Statistics and Probability 430.

Students who are enrolled in the College of Natural Science may complete the alternative track to Integrative Studies in Biological and Physical Sciences that is described in item 1. under the heading Graduation Requirements in the College statement. Certain courses referenced in requirement 3. below may be used to satisfy the alternative track. - The requirements of the College of Natural Science for the Bachelor of Arts degree.

The credits earned in certain courses referenced in requirement 3. below may be counted toward College requirements as appropriate. - The following requirements for the major:
a. The following courses outside the Department of Mathematics (21 credits): (1) One course of at least 3 credits in biological science, entomology, microbiology, physiology, plant biology, or integrative biology. (2) One of the following courses (4 credits): LB 273 Physics I 4 PHY 183 Physics for Scientists and Engineers I 4 (3) One of the following courses (4 credits): CEM 141 General Chemistry 4 CEM 151 General and Descriptive Chemistry 4 CEM 181H Honors Chemistry I 4 LB 171 Principles of Chemistry I 4 (4) Both of the following courses (8 credits): CSE 231 Introduction to Programming I 4 CSE 232 Introduction to Programming II 4 b. Second–year competency in a foreign language. or For students, who have been admitted to the teacher certification program, first-year competency in a foreign language and completion of the Professional Education Courses in the Department of Teacher Education. c. A total of 33 to 40 credits in courses in the Department of Mathematics including: (1) One course from each of the following two groups (6 to 8 credits): (a) MTH 132 Calculus I 3 MTH 152H Honors Calculus 3 LB 118 Calculus I 4 (b) MTH 133 Calculus II 4 MTH 153H Honors Calculus II 3 LB 119 Calculus II 4 (2) One of the following courses (3 or 4 credits): MTH 234 Multivariable Calculus 4 MTH 254H Honors Multivariable Calculus 3 LB 220 Calculus III 4 (3) One of the following two groups (4 or 7 credits): (a) MTH 299 Transitions 4 MTH 309 Linear Algebra I 3 (b) MTH 317H Honors Linear Algebra 4 (4) One course from each of the following groups (6 credits): (a) MTH 310 Abstract Algebra I and Number Theory 3 MTH 418H Honors Algebra I 3 (b) MTH 320 Analysis I 3 MTH 327H Honors Introduction to Analysis 3 (5) All of the following courses (9 credits): MTH 451 Numerical Analysis I 3 MTH 481 Discrete Mathematics I 3 MTH 496 Capstone in Mathematics (W) 3 (6) One of the following courses (3 credits): MTH 452 Numerical Analysis II 3 MTH 482 Discrete Mathematics II 3 (7) One of the following courses (3 credits): MTH 235 Differential Equations 3 MTH 340 Ordinary Differential Equations I 3 MTH 347H Honors Ordinary Differential Equations 3 d. At least one of the following courses (3 credits): Students who select Mathematics 452 or 482 may count the credits toward either requirement 3.c.(6) or 3.d. but not toward both of those requirements. Approval of the Department of Computer Science and Engineering is required to enroll in Computer Science and Engineering 331 and 440. CSE 331 Algorithms and Data Structures 3 CSE 440 Introduction to Artificial Intelligence 3 MTH 360 Theory of Mathematical Interest 3 MTH 415 Applied Linear Algebra 3 MTH 416 Introduction to Algebraic Coding 3 MTH 441 Ordinary Differential Equations II 3 MTH 452 Numerical Analysis II 3 MTH 457 Introduction to Financial Mathematics 3 MTH 482 Discrete Mathematics II 3 STT 351 Probability and Statistics for Engineering 3 STT 430 Introduction to Probability and Statistics 3 STT 441 Probability and Statistics I: Probability 3 STT 455 Actuarial Models I 3 STT 461 Computations in Probability and Statistics 3

**Requirements for the Bachelor of Science Degree in Mathematics**

- The University requirements for bachelor's degrees as described in the
*Undergraduate Education*section of this catalog; 120 credits, including general elective credits, are required for the Bachelor of Science degree in Mathematics.

The University's Tier II writing requirement for the Mathematics major is met by completing Mathematics 396 or 496 and Mathematics 309 or 310 or 418H. Those courses are referenced in item 3.c. below.

Students who are enrolled in the College of Natural Science may complete the alternative track to Integrative Studies in Biological and Physical Sciences that is described in item 1. under the heading Graduation Requirements in the College statement. Certain courses referenced in requirement 3. below may be used to satisfy the alternative track. - The requirements of the College of Natural Science for the Bachelor of Science degree.

The credits earned in certain courses referenced in requirement 3. below may be counted toward College requirements as appropriate. - The following requirements for the major:
a. The following courses outside the Department of Mathematics (20 or 21 credits): (1) One course of at least 3 credits in biological science, entomology, microbiology, physiology, plant biology, or integrative biology. At least 2 credits in laboratory in biological science, chemistry, entomology, microbiology, physics, physiology, plant biology, or integrative biology. (2) One course from each of the following groups (8 or 10 credits): (a) CEM 141 General Chemistry 4 CEM 151 General and Descriptive Chemistry 4 CEM 181H Honors Chemistry I 4 LB 171 Principles of Chemistry I 4 (b) CEM 142 General and Inorganic Chemistry 3 CEM 152 Principles of Chemistry 3 CEM 182H Honors Chemistry II 4 LB 172 Principles of Chemistry II 3 (c) CEM 161 Chemistry Laboratory I 1 CEM 185H Honors Chemistry Laboratory I 2 LB 171L Introductory Chemistry Laboratory I 2 (3) One course from each of the following groups (8 credits): (a) PHY 183 Physics for Scientists and Engineers I 4 LB 273 Physics I 4 (b) PHY 184 Physics for Scientists and Engineers II 4 LB 274 Physics II 4 b. First–year competency in a foreign language or For students who have been admitted to the teacher certification program, completion of the Professional Education Courses in the Department of Teacher Education. c. A total of 36 to 43 credits in courses in the Department of Mathematics including

(36 to 43 credits):(1) One course from each of the following two groups (6 to 8 credits): (a) MTH 132 Calculus I 3 MTH 152H Honors Calculus 3 LB 118 Calculus I 4 (b) MTH 133 Calculus II 4 MTH 153H Honors Calculus II 3 LB 119 Calculus II 4 (2) One of the following courses (4 credits): MTH 234 Multivariable Calculus 4 MTH 254H Honors Multivariable Calculus 4 LB 220 Calculus III 4 (3) One of the following two groups (4 or 7 credits): (a) MTH 299 Transitions 4 MTH 309 Linear Algebra I 3 (b) MTH 317H Honors Linear Algebra 4 (4) The following course (3 credits): MTH 496 Capstone in Mathematics (W) 3 The completion of Mathematics 496 fulfills the department's capstone course requirement. Students in the teacher certification program may substitute Mathematics 396 Capstone in Mathematics for Secondary Education for Mathematics 496. (5) A total of 27 credits in approved Mathematics courses at the 300-level or above. At least four of the approved Mathematics courses must be at the 400-level or above. Mathematics 415 may not be used to fulfill the requirements of the major. Students may use no more than one of Mathematics 309, 314, 317H to satisfy this requirement. One course from a list of approved cognates available in the Department of Mathematics may be used to satisfy this requirement. Statistics and Probability 430 is required for students in the teacher certification program. Either Statistics and Probability 430 or 441 may be substituted for one 300-level mathematics course. The 300-400 level courses as referenced in item 3. c. partially satisfy this requirement. (6) Two of the following courses (6 credits): MTH 310 Abstract Algebra I and Number Theory 3 MTH 411 Abstract Algebra II 3 MTH 418H Honors Algebra I 3 MTH 419H Honors Algebra II 3 Students may not satisfy this requirement with the combination of MTH 411 and MTH 418H. 3 (7) One course from each of the following groups of courses (6 credits): (a) MTH 320 Analysis I 3 MTH 327H Honors Introduction to Analysis 3 (b) MTH 421 Analysis II 3 MTH 429H Honors Real Analysis 3 (8) One of the following courses (3 credits): MTH 330 Higher Geometry 3 MTH 340 Ordinary Differential Equations I 3 MTH 347H Honors Ordinary Differential Equations 3 MTH 432 Axiomatic Geometry 3 Students in the teacher certification program must take either Mathematics 330 or 432. Students not in the teacher certification program must take Mathematics 340 or 347H. Students not in the teacher certification program with prior credit in Mathematics 235 may substitute an approved 400-level Mathematics course for Mathematics 340.

**Requirements for the Bachelor of Arts Degree in Mathematics**

- The University requirements for bachelor's degrees as described in the
*Undergraduate Education*section of this catalog; 120 credits, including general elective credits, are required for the Bachelor of Arts degree in Mathematics.

The University's Tier II writing requirement for the Mathematics major is met by completing Mathematics 396 or 496 and Mathematics 309 or 310 or 418H. Those courses are referenced in items 3. c. (1) and 3. c. (3) below.

Students who are enrolled in the College of Natural Science may complete the alternative track to Integrative Studies in Biological and Physical Sciences that is described in item 1. under the heading Graduation Requirements in the College statement. Certain courses referenced in requirement 3. below may be used to satisfy the alternative track. - The requirements of the College of Natural Science for the Bachelor of Arts degree.

The credits earned in certain courses referenced in requirement 3. below may be counted toward College requirements as appropriate. - The following requirements for the major:
a. The following courses outside the Department of Mathematics (13 credits): (1) One course of at least 3 credits in biological science, entomology, microbiology, physiology, plant biology, or integrative biology. At least 2 credits in laboratory in biological science, chemistry, entomology, microbiology, physics, physiology, plant biology, or integrative biology. (2) One of the following courses (4 credits): LB 273 Physics I 4 PHY 183 Physics for Scientists and Engineers I 4 (3) One of the following courses (4 credits): CEM 141 General Chemistry 4 CEM 151 General and Descriptive Chemistry 4 CEM 181H Honors Chemistry I 4 LB 171 Principles of Chemistry I 4 b. Second–year competency in a foreign language or For students who have been admitted to the teacher certification program, first–year competency in a foreign language and completion of the Professional Education Courses in the Department of Teacher Education. c. A total of 36 to 43 credits in courses in the Department of Mathematics including

(36 to 43 credits):(1) One course from each of the following two groups (6 to 8 credits): (a) MTH 132 Calculus I 3 MTH 152H Honors Calculus 3 LB 118 Calculus I 4 (b) MTH 133 Calculus II 4 MTH 153H Honors Calculus II 3 LB 119 Calculus II 4 (2) One of the following courses (4 credits): MTH 234 Multivariable Calculus 4 MTH 254H Honors Multivariable Calculus 4 LB 220 Calculus III 4 (3) One of the following two groups (4 or 7 credits): (a) MTH 299 Transitions 4 MTH 309 Linear Algebra I 3 (b) MTH 317H Honors Linear Algebra 4 (4) The following course (3 credits): MTH 496 Capstone in Mathematics (W) 3 The completion of Mathematics 496 fulfills the department's capstone course requirement. Students in the teacher certification program may substitute Mathematics 396 Capstone in Mathematics for Secondary Education for Mathematics 496. (5) A total of 27 credits in approved Mathematics courses at the 300–level or above. At least 4 of the approved Mathematics courses must be at the 400–level or above. Mathematics 415 may not be used to fulfill the requirements of the major. Students may use no more than one of MTH 309, 314, 317H to satisfy this requirement. One course from a list of approved cognates available in the Department of Mathematics may be used to satisfy this requirement. Statistics and Probability 430 is required for students in the teacher certification program. Either Statistics and Probability 430 or 441 may be substituted for one 300-level mathematics course. The 300-400 level courses referenced in item 3. c. partially satisfy this requirement. (6) Two of the following courses (6 credits): MTH 310 Abstract Algebra I and Number Theory 3 MTH 411 Abstract Algebra II 3 MTH 418H Honors Algebra I 3 MTH 419H Honors Algebra II 3 Students may not satisfy this requirement with the combination of MTH 411 and MTH 418H. (7) One course from each of the following groups of courses (6 credits): (a) MTH 320 Analysis I 3 MTH 327H Honors Introduction to Analysis 3 (b) MTH 421 Analysis II 3 MTH 429H Honors Real Analysis 3 (8) One of the following courses (3 credits): MTH 330 Higher Geometry 3 MTH 340 Ordinary Differential Equations I 3 MTH 347H Honors Ordinary Differential Equations 3 MTH 432 Axiomatic Geometry 3 Students in the teacher certification program must take either Mathematics 330 or 432. Students not in the teacher certification program must take Mathematics 340 or 347H. Students not in the teacher certification program with prior credit in Mathematics 235 may substitute an approved 400-level Mathematics course for Mathematics 340.

**Requirements for the Bachelor of Arts Degree in Mathematics, Advanced**

- The University requirements for bachelor’s degrees as described in the Undergraduate Education section of this catalog; 120 credits, including general elective credits, are required for the Bachelor of Science degree in Mathematics, Advanced.

The University’s Tier II writing requirement for the Mathematics, Advanced major is met by completing Mathematics 418H and 496. Those courses are referenced in item 3. below.

Students who are enrolled in the College of Natural Science may complete the alternative track to Integrative Studies in Biological and Physical Sciences that is described in item 1. under the heading Graduation Requirements in the College statement. Certain courses referenced in requirement 3. below may be used to satisfy the alternative track. - The requirements of the College of Natural Science for the Bachelor of Arts degree.

The credits earned in certain courses referenced in requirement 3. below may be counted toward College requirements as appropriate. - The following requirements for the major:
a. The following courses outside the Department of Mathematics (12 or 13 credits): (1) One course of at least 3 credits in biological science, entomology, microbiology, physiology, plant biology, or integrative biology. (2) One of the following courses (4 credits): CEM 141 General Chemistry 4 CEM 151 General and Descriptive Chemistry 4 CEM 181H Honors Chemistry I 4 LB 171 Principles of Chemistry I 4 (3) One of the following courses (4 credits): PHY 183 Physics for Scientists and Engineers I 4 PHY 193H Honors Physics I – Mechanics 4 LB 273 Physics I 4 (4) A minimum of 2 credits in laboratory courses in biological science, chemistry, entomology, microbiology, physics, physiology, plant biology, or integrative biology. b. Second-year competency in a foreign language *or*For students who have been admitted to the teacher certification program, completion of the Professional Education Courses in the Department of Teacher Education and first-year competency in a foreign language. c. A total of 34 to 37 credits in courses in the Department of Mathematics including: (1) One of the following courses (3 or 4 credits): MTH 132 Calculus I 3 MTH 152H Honors Calculus I 3 LB 118 Calculus I 4 (2) One of the following courses (4 credits): MTH 133 Calculus II 4 MTH 153H Honors Calculus II 4 LB 119 Calculus II 4 (3) One of the following courses (4 credits): MTH 234 Multivariable Calculus 4 MTH 254H Honors Multivariable Calculus 4 LB 220 Calculus III 4 (4) All of the following courses (25 credits): MTH 317H Honors Linear Algebra 4 MTH 327H Honors Introduction to Analysis 3 MTH 347H Honors Ordinary Differential Equations 3 MTH 418H Honors Algebra I 3 MTH 419H Honors Algebra II 3 MTH 428H Honors Complex Analysis 3 MTH 429H Honors Real Analysis 3 MTH 496 Capstone in Mathematics (W) 3 The completion of Mathematics 496 fulfills the department’s capstone course requirement. d. A minimum of 12 credits in electives. Two courses must be selected from group (1) and two courses from group (2). Any MTH course at the 800-level or above may also satisfy the requirement from group (1). Any MTH course at the 400-level or above may also satisfy the requirement from group (2). Students in the teacher certification program must take MTH 432 to fulfill part of this elective requirement and may not use STT 430 towards fulfillment of this requirement. Any other substitutions must be approved by an advisor for the Mathematics, Advanced program. (1) Two of the following courses (6 credits): MTH 416 Introduction to Algebraic Coding 3 MTH 417 Topics in Number Theory 3 MTH 441 Ordinary Differential Equations II 3 MTH 442 Partial Differential Equations 3 MTH 451 Numerical Analysis I 3 MTH 452 Numerical Analysis II 3 MTH 461 Metric and Topological Spaces 3 MTH 481 Discrete Mathematics I 3 MTH 482 Discrete Mathematics II 3 MTH 492H Undergraduate Thesis (W) 3 (2) Two of the following courses (6 to 8 credits): CMSE 820 Mathematical Foundations of Data Science 3 CMSE 821 Numerical Methods for Differential Equations 3 CMSE 823 Numerical Linear Algebra 3 CSE 425 Introduction to Computer Security 3 CSE 450 Translation of Programming Languages 3 CSE 460 Computability and Formal Language Theory 3 CSE 472 Computer Graphics 3 CSE 802 Pattern Recognition and Analysis 3 CSE 803 Computer Vision 3 CSE 814 Formal Methods in Software Development 3 CSE 830 Design and Theory of Algorithms 3 CSE 835 Algorithmic Graph Theory 3 CSE 847 Machine Learning 3 CSE 860 Foundations of Computing 3 CSE 881 Data Mining 3 EC 820A Econometrics IA 3 EC 820B Econometrics IB 3 PHL 432 Logic and its Metatheory 4 PHY 410 Thermal and Statistical Physics 3 PHY 415 Methods of Theoretical Physics 4 PHY 422 Classical Mechanics II 3 PHY 471 Quantum Physics I 3 PHY 472 Quantum Physics II 3 PHY 480 Computational Physics 3 PHY 481 Electricity and Magnetism I 3 PHY 482 Electricity and Magnetism II 3 STT 861 Theory of Probability and Statistics I 3 STT 862 Theory of Probability and Statistics II 3 STT 881 Theory of Probability I 3 STT 882 Theory of Probability II 3 STT 886 Stochastic Processes and Applications 3

**Requirements for the Bachelor of Science Degree in Mathematics, Advanced**

- The University requirements for bachelor’s degrees as described in the Undergraduate Education section of this catalog; 120 credits, including general elective credits, are required for the Bachelor of Science degree in Mathematics, Advanced.

The University’s Tier II writing requirement for the Mathematics, Advanced major is met by completing Mathematics 418H and 496. Those courses are referenced in item 3. below.

Students who are enrolled in the College of Natural Science may complete the alternative track to Integrative Studies in Biological and Physical Sciences that is described in item 1. under the heading Graduation Requirements in the College statement. Certain courses referenced in requirement 3. below may be used to satisfy the alternative track. - The requirements of the College of Natural Science for the Bachelor of Science degree.

The credits earned in certain courses referenced in requirement 3. below may be counted toward College requirements as appropriate. - The following requirements for the major:
a. The following courses outside the Department of Mathematics (17 to 21 credits): (1) (2) One of the following groups of courses (8 or 10 credits): (a) CEM 141 General Chemistry 4 CEM 142 General and Inorganic Chemistry 3 CEM 161 Chemistry Laboratory I 1 (b) CEM 151 General and Descriptive Chemistry 4 CEM 152 Principles of Chemistry 3 CEM 161 Chemistry Laboratory I 1 (c) CEM 181H Honors Chemistry I 4 CEM 182H Honors Chemistry II 4 CEM 185H Honors Chemistry Laboratory I 2 (d) LB 171 Principles of Chemistry I 4 LB 172 Principles of Chemistry II 3 LB 171L Introductory Chemistry Laboratory I 1 (3) One of the following groups of courses (6 or 8 credits): (a) PHY 183 Physics for Scientists and Engineers I 4 PHY 184 Physics for Scientists and Engineers II 4 (b) PHY 193H Honors Physics I – Mechanics 4 PHY 294H Honors Physics II – Electromagnetism 4 (c) LB 273 Physics I 4 LB 274 Physics II 4 (4) A minimum of 2 credits in laboratory courses in biological science, chemistry, entomology, microbiology, physics, physiology, plant biology, or integrative biology. b. First-year competency in a foreign language *or*For students who have been admitted to the teacher certification program, completion of the Professional Education Courses in the Department of Teacher Education. c. A total of 34 to 37 credits in courses in the Department of Mathematics including: (1) One of the following courses (3 or 4 credits): MTH 132 Calculus I 3 MTH 152H Honors Calculus I 3 LB 118 Calculus I 4 (2) One of the following courses (4 credits): MTH 133 Calculus II 4 MTH 153H Honors Calculus II 4 LB 119 Calculus II 4 (3) One of the following courses (4 credits): MTH 234 Multivariable Calculus 4 MTH 254H Honors Multivariable Calculus 4 LB 220 Calculus III 4 (4) All of the following courses (25 credits): MTH 317H Honors Linear Algebra 4 MTH 327H Honors Introduction to Analysis 3 MTH 347H Honors Ordinary Differential Equations 3 MTH 418H Honors Algebra I 3 MTH 419H Honors Algebra II 3 MTH 428H Honors Complex Analysis 3 MTH 429H Honors Real Analysis 3 MTH 496 Capstone in Mathematics (W) 3 The completion of Mathematics 496 fulfills the department’s capstone course requirement. d. A minimum of 12 credits in electives. Two courses must be selected from group (1) and two courses from group (2). Any MTH course at the 800-level or above may also satisfy the requirement from group (1). Any MTH course at the 400-level or above may also satisfy the requirement from group (2). Students in the teacher certification program must take MTH 432 to fulfill part of this elective requirement and may not use STT 430 towards fulfillment of this requirement. Any other substitutions must be approved by an advisor for the Mathematics, Advanced program. (1) Two of the following courses (6 credits): MTH 416 Introduction to Algebraic Coding 3 MTH 417 Topics in Number Theory 3 MTH 441 Ordinary Differential Equations II 3 MTH 442 Partial Differential Equations 3 MTH 451 Numerical Analysis I 3 MTH 452 Numerical Analysis II 3 MTH 461 Metric and Topological Spaces 3 MTH 481 Discrete Mathematics I 3 MTH 482 Discrete Mathematics II 3 MTH 492H Undergraduate Thesis (W) 3 (2) Two of the following courses (6 to 8 credits): CMSE 820 Mathematical Foundations of Data Science 3 CMSE 821 Numerical Methods for Differential Equations 3 CMSE 823 Numerical Linear Algebra 3 CSE 425 Introduction to Computer Security 3 CSE 450 Translation of Programming Languages 3 CSE 460 Computability and Formal Language Theory 3 CSE 472 Computer Graphics 3 CSE 802 Pattern Recognition and Analysis 3 CSE 803 Computer Vision 3 CSE 814 Formal Methods in Software Development 3 CSE 830 Design and Theory of Algorithms 3 CSE 835 Algorithmic Graph Theory 3 CSE 847 Machine Learning 3 CSE 860 Foundations of Computing 3 CSE 881 Data Mining 3 EC 820A Econometrics IA 3 EC 820B Econometrics IB 3 PHL 432 Logic and its Metatheory 4 PHY 410 Thermal and Statistical Physics 3 PHY 415 Methods of Theoretical Physics 4 PHY 422 Classical Mechanics II 3 PHY 471 Quantum Physics I 3 PHY 472 Quantum Physics II 3 PHY 480 Computational Physics 3 PHY 481 Electricity and Magnetism I 3 PHY 482 Electricity and Magnetism II 3 STT 861 Theory of Probability and Statistics I 3 STT 862 Theory of Probability and Statistics II 3 STT 881 Theory of Probability I 3 STT 882 Theory of Probability II 3 STT 886 Stochastic Processes and Applications 3

The Minor in Mathematics, which is administered by the Department of Mathematics, will broaden students’ understanding and application of mathematical concepts to their chosen field of study.

The minor is available as an elective to students who are enrolled in bachelor’s degree programs at Michigan State University other than the Bachelor of Arts and Bachelor of Science Degree in Mathematics. With the approval of the department and college that administer the student’s degree program, the courses that are used to satisfy the minor may also be used to satisfy the requirements for the bachelor’s degree.

Students who plan to complete the requirements of the minor should consult the undergraduate advisor in the Department of Mathematics.

Requirements for the Minor in Mathematics

Complete the following (21 to 28 credits):

1. | One of the following courses (3 or 4 credits): | ||||||

LB | 118 | Calculus I | 4 | ||||

MTH | 132 | Calculus I | 3 | ||||

MTH | 152H | Honors Calculus I | 3 | ||||

2. | One of the following courses (3 or 4 credits): | ||||||

LB | 119 | Calculus II | 4 | ||||

MTH | 133 | Calculus II | 4 | ||||

MTH | 153H | Honors Calculus II | 3 | ||||

3. | One of the following courses (3 or 4 credits): | ||||||

LB | 220 | Calculus III | 4 | ||||

MTH | 234 | Multivariable Calculus | 4 | ||||

MTH | 254H | Honors Multivariable Calculus | 3 | ||||

4. | One of the following groups of courses (3 to 7 credits): | ||||||

(a) | MTH | 299 | Transitions | 4 | |||

MTH | 309 | Linear Algebra I | 3 | ||||

(b) | MTH | 317H | Advanced Linear Algebra | 3 | |||

5. | All of the following courses (9 credits): | ||||||

MTH | 310 | Abstract Algebra I and Number Theory | 3 | ||||

MTH | 320 | Analysis I | 3 | ||||

One 400-level mathematics course approved by the student's advisor | 3 |

The Minor in Actuarial Science, which is administered by the Department of Mathematics within the College of Natural Science, is available as an elective to students who are enrolled in any bachelor’s degree program at Michigan State University. This minor complements a number of major fields such as mathematics, statistics and probability, finance, and economics. It is intended to prepare students for work in insurance companies, banks, investment firms, government work, hospitals and business firms where there is a need to weigh the financial consequences of risk. The Minor in Actuarial Science prepares students for two of the examinations of the Society of Actuaries (SOA): Exam P/1 and Exam FM/2. With the approval of the department that administers the student’s degree program, courses that are used to satisfy the requirements for the minor may also be used to satisfy the requirements for the bachelor’s degree.

**Requirements for the Minor in Actuarial Science**

The student must complete all of the following courses (21 credits):

1. | All of the following courses (18 credits): | ||||||

FI | 311 | Financial Management | 3 | ||||

FI | 321 | Theory of Investments | 3 | ||||

MTH | 360 | Theory of Mathematical Interest | 3 | ||||

MTH | 361 | Financial Mathematics for Actuaries I | 3 | ||||

STT | 441 | Probability and Statistics I: Probability | 3 | ||||

STT | 455 | Actuarial Models I | 3 | ||||

2. | One of the following courses (3 credits): | ||||||

MTH | 457 | Introduction to Financial Mathematics | 3 | ||||

STT | 442 | Probability and Statistics II: Statistics | 3 |

The mathematics disciplinary majors leading to the Bachelor of Arts and Bachelor of Science degrees are available for teacher certification. The mathematics, advanced major leading to the Bachelor of Arts or Bachelor of Science degree is also available for secondary teacher certification.

A mathematics-elementary and mathematics-secondary disciplinary minor are also available for teacher certification.

Students who elect a mathematics or mathematics, advanced disciplinary major or the mathematics-elementary or mathematics-secondary disciplinary minor must contact the Department of Mathematics.

For additional information, refer to the statement on *TEACHER CERTIFICATION* in the *Department of Teacher Education* section of this catalog.

The Department of Mathematics is ranked a tier-one program by the National Research Council rankings and conducts world-class research in a broad spectrum of mathematical endeavors. At the highest level, the department offers the graduate degrees of Doctor of Philosophy in Mathematics and Doctor of Philosophy in Applied Mathematics, which open the door to research careers in universities, national laboratories, and industry. We also offer graduate work leading to Master of Science degrees in Mathematics and in Applied Mathematics, as well as a Master of Arts for Teachers degree. Our Professional Master's program in Industrial Mathematics has an exemplary record of preparing students for careers in industry.

In addition to meeting the requirements of the university and of the College of Natural Science, students must meet the requirements specified below.

**Admission**

To be admitted to the Master of Science degree program in applied mathematics, a person should have completed (1) the mathematics or applied mathematics courses normally required for the bachelor's degree with a major in mathematics, physics, or engineering, (2) a minimum of a year's work in mathematical analysis at the senior year level, and (3) courses in matrices and linear algebra.

**Requirements for the Master of Science Degree in Applied Mathematics**

The student must complete a total of 30 credits for the degree under Plan B (without thesis). The student's program of study must be approved by the student's academic advisor and must include:

- At least 24 credits in mathematics courses including:
- At least 6 credits from the following courses: Mathematics 818, 819, 828, 829, 848, 849, 868, 869.
- At least 12 credits in 800–level applied mathematics courses including 6 credits in one of the following groups of courses: Mathematics 841, 842; 848, 849; 850, 851; or 880, 881.

The completion of Mathematics 848 and 849 may be used to satisfy**either**the requirement referenced in item 1 a.**or**the requirement referenced in item 1. b., but**not**both of those requirements.

- At least 18 credits in 800–900 level courses.

In addition to meeting the requirements of the University and of the College of Natural Science, students must meet the requirements specified below.

**Admission**

Regular admission to the Doctor of Philosophy degree program in applied mathematics presupposes academic preparation equivalent to a Master of Science degree with a major in mathematics with a grade–point average of 3.00 or better. However, a student with a bachelor's degree whose undergraduate preparation is strong may be admitted directly to the program upon passing a qualifying examination.

**Requirements for the Doctor of Philosophy Degree in Applied Mathematics**

The student must:

- Pass the qualifying examination.
- Complete at least 30 credits in approved 800–900 level mathematics courses excluding courses taken in preparation for the qualifying examination and Mathematics 999; at least 18 of the 30 credits must be in applied mathematics courses.
- Present at least two seminars acceptable to the faculty.
- Pass the comprehensive examination.
- Demonstrate a reading knowledge of one foreign language, normally from among French, German, and Russian, sufficient to read the mathematical literature written in that language.
- Complete a dissertation in applied mathematics.

For detailed information regarding the qualifying and comprehensive examinations, contact the Department of Mathematics.

The degree of Master of Science in Industrial Mathematics is designed to produce generalized problem solvers of great versatility, capable of moving within an organization from task to task. The graduate will have acquired not only the standard mathematical and statistical tools and computer science principles to strengthen data analytic skills, but also the basic ideas of engineering and business, and will have received training in project development and in modes of industrial communication. The program is designed for students planning careers in business, government or industry.

**Admission**

To be admitted to the Master of Science in Industrial Mathematics program, a person should have completed (1) the mathematics or applied mathematics courses normally required for the bachelor’s degree with a major in mathematics, statistics, economics, physics or engineering, (2) courses at the senior level in mathematical analysis, linear algebra and differential equations, and (3) have some familiarity with mathematical software programs such as Mathematica, Matlab, etc.

Students entering the program are expected to have a mathematical preparation at the level of Mathematics 421, 414 and 442. Students with deficiencies may be required to take additional course work.

**Requirements for the Master of Science Degree in Industrial Mathematics**

In addition to meeting the requirements of the University and the College of Natural Science, the student must complete a total of 30 credits for the degree under Plan B (without thesis). The student’s program of study must be approved by the student’s academic advisor, including:

1. | The following requirements for the major (30 credits): | ||||||

a. | Both of the following courses: | ||||||

MTH | 843 | Survey of Industrial Mathematics | 3 | ||||

MTH | 844 | Projects in Industrial Mathematics | 3 | ||||

b. | A minimum of two of the following courses: | ||||||

MTH | 810 | Error-Correcting Codes | 3 | ||||

MTH | 841 | Boundary Value Problems I | 3 | ||||

MTH | 842 | Boundary Value Problems II | 3 | ||||

MTH | 847 | Partial Differential Equations I | 3 | ||||

MTH | 848 | Ordinary Differential Equations | 3 | ||||

MTH | 849 | Partial Differential Equations | 3 | ||||

MTH | 850 | Numerical Analysis I | 3 | ||||

MTH | 851 | Numerical Analysis II | 3 | ||||

MTH | 852 | Numerical Methods for Ordinary Differential Equations | 3 | ||||

MTH | 880 | Combinatorics I | 3 | ||||

MTH | 881 | Graph Theory | 3 | ||||

c. | A minimum of two of the following courses: | ||||||

STT | 801 | Design of Experiments | 3 | ||||

STT | 802 | Statistical Computation | 3 | ||||

STT | 843 | Multivariate Analysis | 3 | ||||

STT | 844 | Time Series Analysis | 3 | ||||

STT | 847 | Analysis of Survival Data | 3 | ||||

STT | 861 | Theory of Probability and Statistics I | 3 | ||||

STT | 862 | Theory of Probability and Statistics II | 3 | ||||

STT | 863 | Statistics Methods I | 3 | ||||

STT | 864 | Statistics Methods II | 3 | ||||

STT | 866 | Spatial Data Analysis | 3 | ||||

STT | 875 | R Programming for Data Sciences | 3 | ||||

STT | 886 | Stochastic Processes and Applications | 4 | ||||

STT | 888 | Stochastic Models in Finance | 3 | ||||

d. | At least two of the following courses: | ||||||

CMSE | 801 | Introduction to Computational Modeling | 3 | ||||

CMSE | 802 | Methods in Computational Modeling | 3 | ||||

CMSE | 820 | Mathematical Foundations of Data Science | 3 | ||||

CMSE | 821 | Numerical Methods for Differential Equations | 3 | ||||

CMSE | 822 | Parallel Computing | 3 | ||||

CMSE | 823 | Numerical Linear Algebra | 3 | ||||

CSE | 802 | Pattern Recognition and Analysis | 3 | ||||

CSE | 803 | Computer Vision | 3 | ||||

CSE | 830 | Design and Theory of Algorithms | 3 | ||||

CSE | 835 | Algorithmic Graph Theory | 3 | ||||

CSE | 836 | Probabilistic Models and Algorithms in Computational Biology | 3 | ||||

CSE | 841 | Artificial Intelligence | 3 | ||||

CSE | 847 | Machine Learning | 3 | ||||

CSE | 860 | Foundations of Computing | 3 | ||||

CSE | 872 | Advanced Computer Graphics | 3 | ||||

CSE | 880 | Advanced Database Systems | 3 | ||||

CSE | 881 | Data Mining | 3 | ||||

CSE | 885 | Artificial Neural Networks | 3 | ||||

EC | 811A | Mathematical Applications in Economics | 2 | ||||

EC | 811B | The Structure of Economic Analysis | 2 | ||||

EC | 812A | Microeconomics I | 3 | ||||

EC | 812B | Microeconomics II | 3 | ||||

EC | 813A | Macroeconomics I | 3 | ||||

EC | 813B | Macroeconomics II and its Mathematical Foundations | 4 | ||||

EC | 820A | Econometrics IA | 3 | ||||

EC | 820B | Econometrics IB | 3 | ||||

EC | 821A | Cross Section and Panel Data Econometrics I | 3 | ||||

EC | 821B | Cross Section and Panel Data Econometrics II | 3 | ||||

EC | 822A | Time Series Econometrics I | 3 | ||||

EC | 822B | Time Series Econometrics II | 3 | ||||

ECE | 848 | Evolutionary Computation | 3 | ||||

ECE | 863 | Analysis of Stochastic Systems | 3 | ||||

ME | 830 | Fluid Mechanics I | 3 | ||||

ME | 840 | Computational Fluid Dynamics and Heat Transfer | 3 | ||||

ME | 872 | Finite Element Method | 3 | ||||

MKT | 805 | Marketing Management | 2 | ||||

MKT | 806 | Marketing Research for Decision Making | 3 | ||||

MKT | 816 | Marketing Analysis | 3 | ||||

MKT | 819 | Advanced Marketing Research | 3 | ||||

MKT | 864 | Data Mining in Marketing | 3 | ||||

SCM | 800 | Supply Chain Management | 3 | ||||

SCM | 815 | Emerging Topics in Supply Management | 3 | ||||

SCM | 826 | Manufacturing Design and Analysis | 1.5 | ||||

SCM | 833 | Decision Support Models | 2 | ||||

SCM | 843 | Sustainable Supply Chain Management | 2 | ||||

SCM | 853 | Operations Strategy | 2 | ||||

SCM | 854 | Integrated Logistics Systems | 1.5 | ||||

e. | Completion of a Certificate Program in Project Management. This requires completion of PHM 857 Project Management, covering such topics as formal project management culture, principles, knowledge areas, and terminology. It will normally be undertaken during the first year of enrollment with the opportunity to use the credit-no credit grading system. Certification will also require participation in Industrial Mathematics-specific discussion sessions. After the completion of the certificate program is approved by the instructors, the Industrial Mathematics Program, and the Associate Dean of the College of Natural Science, the Office of the Registrar will enter on the student’s academic record the name of the certificate program and the date it was completed. This certification will appear on the student’s transcript upon completion of the requirements for the degree program. |

In addition to meeting the requirements of the University and of the College of Natural Science, students must meet the requirements specified below.

**Admission **

To be admitted to the Master of Arts for Teachers degree program in mathematics, a person should have (1) at least one year of calculus and (2) at least 10 credits of acceptable junior and senior mathematics courses. Normally these 10 credits should include courses in advanced calculus and modern algebra. The candidate should also possess, or be a candidate for, teacher certification.

**Requirements for the Master of Arts for Teachers Degree in Mathematics**

The student must complete a total of 30 credits for the degree under Plan B (without thesis). The student's program of study must be approved by the student's academic advisor and must include:

- At least 9 credits from the following courses: Mathematics 801, 802A, 802B, and 903.
- At least 15 additional credits in mathematics or statistics courses including one course sequence, such as algebra or discrete mathematics, from a list of approved courses that is available in the Department of Mathematics.
- Course work in each of the following five areas of mathematics: geometry, algebra, analysis, discrete mathematics, and probability and statistics. Courses completed while enrolled in a bachelor's degree program may be used to satisfy this requirement.

In addition to meeting the requirements of the university and of the College of Natural Science, students must meet the requirements specified below.

**Admission **

To be admitted to the Master of Science degree program in mathematics, a person should have (1) at least one year of calculus and (2) at least 10 credits of acceptable junior and senior mathematics courses. Normally these 10 credits should include courses in advanced calculus and modern algebra.

**Requirements for the Master of Science Degree in Mathematics**

The student must complete a total of 30 credits for the degree under Plan B (without thesis). The student's program of study must be approved by the student's academic advisor and must include:

- At least 24 credits in mathematics courses including at least 6 credits from the following courses: Mathematics 818, 819, 828, 829, 848, 849, 868, 869.
- At least 18 credits in 800–900 level courses.

In addition to meeting the requirements of the university and of the College of Natural Science, students must meet the requirements specified below.

**Admission **

Regular admission to the Doctor of Philosophy degree program in mathematics presupposes academic preparation equivalent to a Master of Science degree with a major in mathematics with a grade–point average of 3.00 or better. However, a student with a bachelor's degree whose undergraduate preparation is strong may be admitted directly to the program upon passing a qualifying examination.

**Requirements for the Doctor of Philosophy Degree in Mathematics**

The student must:

- Pass the qualifying examination.
- Complete at least 30 credits in approved 800–900 level mathematics courses excluding courses taken in preparation for the qualifying examination and Mathematics 999.
- Present at least two seminars acceptable to the faculty.
- Pass the comprehensive examination.
- Demonstrate a reading knowledge of one foreign language, normally from among French, German, and Russian, sufficient to read the mathematical literature written in that language.

For detailed information regarding the qualifying and comprehensive examinations, contact the Department of Mathematics.