This information is part of the Colgate University catalog, 2024-25.

Faculty |
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Professors Robertson (Chair), Saracino, SchultAssociate Professors Chen, Christensen, Cipolli, Davis, Jiménez Bolaños, SeoAssistant Professors Isham, Ma, Moore, Sosa CastilloVisiting Assistant Professors Brittenham, GuSenior Lecturer Tatangelo |

There are many good reasons to study mathematics: preparation for a career, use in another field, or the beauty of the subject itself. Students at Colgate who major in mathematics go on to careers in medicine, law, or business administration as well as areas of industry and education having an orientation in science. Non-majors often require mathematical skills to carry on work in other disciplines, and all students can use the study of mathematics to assist them in forming habits of precise expression, in developing their ability to reason logically, and in learning how to deal with abstract concepts. There are also many people who view mathematics as an art form, to be studied for its own intrinsic beauty.

All mathematics courses are open to qualified students. Entering first-year students who have successfully completed at least three years of secondary school mathematics, including trigonometry, should be adequately prepared for MATH 161. Students who have studied calculus in secondary school are typically ready to enter MATH 162 or MATH 163.

Students who are planning to undertake graduate study in mathematics are advised to take MATH 485 and MATH 487.

### Course Information

The following classification scheme is used for MATH courses:

100-149: Only requires knowledge of mathematics before Calculus

150-199: Calculus-level knowledge and/or sophistication

200-249: Linear Algebra level (gentle transition-type course)

250-299: Transition to the major level

300-349: Courses with requirements at Math 150-249 level

350-399: Courses with requirements at the Math 250-299 level

400-449: Courses with requirements at the Math 300-349 level

450-474: Courses with requirements at the Math 350-399 level

475-484: Research experience seminars

485-499: Advanced material

The expected rotation schedule of course offerings is described on the Department of Mathematics webpage.

### Honors and High Honors

To be considered for honors in Mathematics or in Applied Mathematics, a student must achieve a 3.3 GPA in the respective major. In order to be considered for high honors, a 3.7 GPA in the major is required. For both honors and high honors, completion of a course numbered 400 or above besides 481-483 is required.

Honors / High Honors are attained by a student's production and defense of a thesis of distinction. The student's thesis adviser puts forward the thesis for honors consideration. Subsequently, a committee of three faculty members is formed, one being the student's thesis advisor, the others chosen by the department. The student must give a defense of the thesis. The committee of three, with other faculty members acting in an advisory capacity with a recommendation, then grades the project, consisting of the thesis and defense. In order for honors to be granted, the committee of three must grade the project as A- or better. In the event all three grade the project as A or better, high honors will be granted.

Joint theses are allowed but will not normally be considered for honors. Exceptions may be made with departmental permission.

As a reminder to the student writing theses for two different departments: Colgate's Honor Code states that substantial portions of the same academic work may not be submitted for credit or honors more than once without the permission of the instructor(s).

### Awards

*The Allen First-Year Mathematical Prize* — awarded for excellence in mathematical work on the basis of scores attained on the first year prize exam covering material from Math 161 and 162.

*The Edwin J. Downie '33 Award for Mathematics* — created in memory of Edwin J. Downie '33, Professor of Mathematics Emeritus, given annually to a senior majoring in mathematics who has made outstanding contributions to the mathematics department through exemplary leadership, service, and achievement.

*The Osborn Mathematics Prizes* — established in honor of Professor Lucien M. Osborn, Class of 1847, to be awarded to students based on their performance on the Osborn Prize Exams covering material from exactly two of the following courses: MATH 375, MATH 376, MATH 377.

*The Sisson Mathematics Prizes* — established in honor of Eugene Pardon Sisson, a teacher of mathematics in the academy 1873–1912, awarded to a student who maintains a high average in one or more 200-level mathematics courses.

### Calculus Placement

Students should review the MATH 161, MATH 162, and MATH 163 course descriptions for information on topics and prerequisites, or consult with a department faculty member. In general, students are encouraged to enroll in a higher-level course. Students may drop back from MATH 162 to MATH 161 within the first three weeks, subject to available space in an acceptable MATH 161 section.

### Advanced Placement

Students who have taken the Calculus-BC, Calculus-AB, or Statistics Advanced Placement exam of the College Entrance Examination Board will be granted credit according to the following policy:

- Students earning 4 or 5 on the Calculus-BC Advanced Placement exam will receive credit for MATH 161 and MATH 162. Students earning 3 on the Calculus BC exam will receive credit only for MATH 161.
- Students earning 4 or 5 on the Calculus-AB Advanced Placement exam will receive credit for MATH 161.
- Students earning 4 or 5 on the Statistics Advanced Placement exam will receive credit for MATH 105.
- There are no other circumstances under which a student will receive credit at Colgate for a mathematics course taken in high school.

### Transfer Credit

Transfer credit for a mathematics course taken at another college may be granted with pre-approval from the department chair.

The following courses count toward the appropriate major or minor in Mathematics or Applied Mathematics only if passed at Colgate by completing a regularly scheduled course: MATH 250, MATH 260, MATH 375, MATH 376, MATH 377.

At most, two transfer or independent studies courses may be counted toward a major or minor.

### International Exam Transfer Credit

Transfer credit and/or placement appropriate to academic development of a student may be granted to incoming first year students who have achieved a score on an international exam (e.g., A-Levels, International Baccalaureate) that indicates a level of competence equivalent to the completion of a specific course in the department. See the registrar's office prematriculation web page for more information.

### Related Majors/Minors

### Teacher Certification

The Department of Educational Studies offers a teacher education program for majors in mathematics who are interested in pursuing a career in elementary or secondary school teaching. Please refer to Educational Studies.

### Study Groups

Colgate sponsors several study-abroad programs that can support continued work toward a major in mathematics. These include, but are not limited to, the Wales Study Group (U.K.), the Australia Study Group, the Australia II Study Group, the Singapore Exchange Program, and the Manchester Study Group (U.K.). For more information about these programs, see Off-Campus Study.

### Majors and Minors

#### Major

#### Minor

### Courses

- MATH 105 - Introduction to Statistics
- MATH 161 - Calculus I
- MATH 162 - Calculus II
- MATH 163 - Calculus III
- MATH 214 - Linear Algebra
- MATH 240L - Computational Statistics with R Lab
- MATH 240 - Computational Statistics with R
- MATH 250 - Number Theory and Mathematical Reasoning
- MATH 260L - Computational Mathematics Lab
- MATH 260 - Computational Mathematics
- MATH 291 - Independent Study
- MATH 302 - Systems Biology
- MATH 307 - Geometry
- MATH 308 - Differential Equations
- MATH 310 - Combinatorial Problem Solving
- MATH 312 - Math Modeling: Social Sciences
- MATH 313 - Functions of a Complex Variable
- MATH 315 - Mathematical Biology
- MATH 316 - Probability
- MATH 354 - Data Analysis I - Applied Linear Models
- MATH 360 - Graph Theory
- MATH 362 - Topology
- MATH 375 - Abstract Algebra I
- MATH 376 - Numerical Analysis
- MATH 377 - Real Analysis I
- MATH 391 - Independent Study
- MATH 408 - Partial Differential Equations
- MATH 410 - Ramsey Theory
- MATH 414 - Matroids
- MATH 416 - Mathematical Statistics
- MATH 417 - Brownian Motion & Stochastic Calculus
- MATH 448 - Nonlinear Dynamics & Chaos
- MATH 450 - Number Theory II
- MATH 454 - Data Analysis II - Nonlinear Model Inference
- MATH 460 - Hilbert and Banach Spaces
- MATH 481 - Investigations in Computational Biology
- MATH 482 - Senior Seminar: Applied Mathematics
- MATH 483 - Senior Seminar: Mathematics
- MATH 485 - Abstract Algebra II
- MATH 487 - Real Analysis II
- MATH 489 - Axiomatic Set Theory
- MATH 491 - Independent Study
- MATH 499 - Mathematical Logic