Mathematics (MATH)
Mathematics has long been the language of the natural sciences and has been studied for its own sake since ancient times. Statistics is the foundational tool for understanding and analyzing data from a wide variety of sources and also an area of active research in its own right. An understanding of the basics of calculus, statistics and linear algebra has become a requirement for proficiency in many of the social sciences. The study of mathematics or statistics has rewards because accomplishment in the subjects, even at a relatively elementary level, requires and promotes clarity of both thought and expression. For many, the study of mathematics offers entrance into an exciting world of challenges where beauty and utility coexist in balanced harmony. The study of statistics is the bridge between data and understanding and offers insights otherwise unobtainable.
A major in mathematics, applied mathematics, or statistics opens the door to a whole range of employment opportunities as the analytical skills that a student develops in pursuing these majors are greatly valued by potential employers. There are, for example, excellent career prospects in actuarial work and in the rapidly growing areas of analytics, biomathematics and biostatistics, modeling (in industry, government and finance) and cryptology (in banking, television, the Internet and elsewhere). These majors can also be seen as the first step toward obtaining a graduate degree in one of the mathematical sciences, or constitute preparation for a professional degree program in a field such as education, medicine, law or business.
Mathematics Majors and Statistics Majors
The Mathematics Department offers four majors. Students may earn a Bachelor of Arts in Mathematics, a Bachelor of Science in Mathematics, a Bachelor of Science in Applied Mathematics or a Bachelor of Science in Statistics. The choice of degree program depends largely upon the student’s mathematical or statistical objectives and interests in fields other than mathematics. Students with strong interests outside mathematics have options including a Bachelor of Science in Applied Mathematics, a Bachelor of Arts in Mathematics or a Bachelor of Science in the Mathematical Economics program.
Students in each major complete an introductory year of calculus during their first year, or fulfill this requirement by achieving a high score on the Advanced Placement Test of the College Entrance Examination Board. Students with a strong interest in a career in mathematics or science – and in particular, students planning to continue on to Ph.D. programs in the mathematical sciences – are strongly advised to take courses beyond the minimum requirements for the major. Since the number of courses to be taken in any one department is restricted to 12 for a Bachelor of Arts degree, such students are advised to choose one of the Bachelor of Science majors.
Students pursuing a BS in Statistics or a BS in Mathematics are eligible to pursue a BA in Data Science as a co-major. Complementing the depth a student receives from their primary major, the BA in Data Science provides breadth across the interdisciplinary field of data science. The major is not intended as – nor can it be declared as – a stand-alone course of study.
Bachelor of Arts in Mathematics
The Bachelor of Arts in Mathematics major consists of eight mathematics courses beyond the introductory year of calculus, plus one additional course in a related field and a Culminating Experience.
Of the eight mathematics courses beyond the introductory year of calculus, five are specified:
| Program Requirements | ||
| MATH 211 | Calculus III | 1 |
| MATH 245 | Linear Algebra | 1 |
| MATH 280 | Logic, Sets, and Proofs | 1 |
| MATH 308 | Real Analysis I | 1 |
| MATH 320 | Abstract Algebra I | 1 |
| Electives | ||
| Three electives at the 300 or 400-level | 3 | |
| Related Field Course | ||
| Select one of the following: | 1 | |
Fourth mathematics course at the 300 or 400-level | ||
| The Teaching of Mathematics in Secondary Schools | ||
| Differential Equations | ||
| Statistics I | ||
| Statistics II | ||
| Topics in Applied Mathematics | ||
| Data Visualization & Computing | ||
An additional full-credit course in which college-level mathematics or statistics plays a major role. 1 | ||
| A Culminating Experience 2 | ||
| Total Credits: 11-12 | ||
- 1
Examples include any computer science or science course (beyond those required for all liberal arts students), including nearly all courses in computer science or physics at or above the 200-level, or an appropriate course from humanities, social sciences or engineering in which mathematics plays a significant role at a reasonable level of sophistication.
- 2
The requirement for a Culminating Experience within the major may be satisfied in any of the following ways: (1) taking a full-credit, 400-level mathematics course; or (2) completing a guided research project, such as an honors thesis, in mathematics, statistics, mathematics education or applied mathematics. This project should extend beyond one semester and include an initial proposal, a final product and a public presentation of results; or (3) completing student teaching for secondary certification. The Culminating Experience may be non-credit bearing. Students earning a Bachelor of Arts in Mathematics may count a 400-level mathematics course both as their mathematics-related course and as the Culminating Experience. The Culminating Experience may be undertaken in the spring of junior year or the fall or spring of senior year.
The mathematics department chair shall make the determination of whether or not a particular course outside the mathematics department may count as the course in a related field.
The College of Arts & Sciences Core Curriculum disciplinary depth requirements for the bachelor of arts major are satisfied as follows:
- writing within the major in MATH 280 Logic, Sets, and Proofs, MATH 308 Real Analysis I and MATH 320 Abstract Algebra I (all W2 courses);
- information literacy in MATH 308 Real Analysis I and MATH 320 Abstract Algebra I;
- formal presentation as part of the culminating experience.
Students with a special interest in pure mathematics or statistics may earn formal concentration in these areas by completing an appropriate suite of 300 and 400-level courses, as described below.
Pure Mathematics Concentration
| MATH 345 | Advanced Linear Algebra | 1 |
| MATH 409 | Real Analysis II | 1 |
| MATH 446 | Abstract Algebra II | 1 |
| Select two of the following: | 2 | |
| Theory of Numbers | ||
| Topology | ||
| Complex Analysis | ||
Statistics Concentration
| MATH 303 | Probability | 1 |
| MATH 304 | Statistical Inference Theory | 1 |
| Three courses from the following, subject to: at least one of MATH 405 and MATH 407, and no more than one of MATH 345 and MATH 409 may count toward this requirement. | 3 | |
| Bayesian Statistics | ||
| Advanced Linear Algebra | ||
| Modern Data Analysis | ||
| Statistical Modeling | ||
| Statistical Design of Scientific Studies | ||
| Real Analysis II | ||
Bachelor of Science in Mathematics
The Bachelor of Science in Mathematics major requires 10 mathematics courses beyond the introductory year of calculus, a computing course, two physics courses, an additional lab science course and a Culminating Experience.
Six of the 10 mathematics courses are specified:
| Program Requirements | ||
| MATH 211 | Calculus III | 1 |
| MATH 212 | Differential Equations | 1 |
| MATH 245 | Linear Algebra | 1 |
| MATH 280 | Logic, Sets, and Proofs | 1 |
| MATH 308 | Real Analysis I | 1 |
| MATH 320 | Abstract Algebra I | 1 |
| Electives | ||
| Four mathematics electives at the 300 or 400-level | 4 | |
| PHYS 211 | Classical and Modern Physics I | 1 |
| Select one of the following: | 1 | |
| Classical and Modern Physics II | ||
or PHYS 212E | Classical and Modern Physics II | |
| CSCI 203 | Introduction to Computer Science | 1 |
| One additional laboratory science course. 3 | 1 | |
| A Culminating Experience. 4 | ||
- 3
The additional laboratory science course may be chosen from any discipline in the natural sciences or from computer science. Any course in physics beyond PHYS 212 Classical and Modern Physics II, and any laboratory course in computer science beyond CSCI 203 Introduction to Computer Science, may be chosen.
- 4
The requirement for a Culminating Experience within the major may be satisfied in any of the following ways: (1) taking a full credit 400-level mathematics course; or (2) completing a guided research project, such as an honors thesis, in mathematics, statistics, mathematics education, or applied mathematics. This project should extend beyond one semester and include an initial proposal, a final product, and a public presentation of results; or (3) completing student teaching for secondary certification. The Culminating Experience may be non-credit bearing. The Culminating Experience cannot double-count as one of the mathematics electives required in the major. The course for a Culminating Experience may be undertaken in the spring of junior year or the fall or spring of senior year.
The College of Arts & Sciences Core Curriculum disciplinary depth requirements for the bachelor of science major are satisfied as follows:
- writing within the major in MATH 280 Logic, Sets, and Proofs, MATH 308 Real Analysis I and MATH 320 Abstract Algebra I (all W2 courses);
- information literacy in MATH 308 Real Analysis I and MATH 320 Abstract Algebra I;
- formal presentation as part of the culminating experience.
Students with a special interest in pure mathematics or statistics may earn formal concentration in these areas by completing an appropriate suite of 300 and 400-level courses, as described below. In particular, those intending to pursue graduate study in mathematics or statistics should plan to complete the relevant concentration.
Pure Mathematics Concentration
| MATH 345 | Advanced Linear Algebra | 1 |
| MATH 409 | Real Analysis II | 1 |
| MATH 446 | Abstract Algebra II | 1 |
| Select two of the following: | 2 | |
| Theory of Numbers | ||
| Topology | ||
| Complex Analysis | ||
Statistics Concentration
| MATH 303 | Probability | 1 |
| MATH 304 | Statistical Inference Theory | 1 |
| Three courses from the following, subject to: at least one of MATH 405 and MATH 407, and no more than one of MATH 345 and MATH 409 may count toward this requirement. | 3 | |
| Bayesian Statistics | ||
| Advanced Linear Algebra | ||
| Modern Data Analysis | ||
| Statistical Modeling | ||
| Statistical Design of Scientific Studies | ||
| Real Analysis II | ||
A sample sequence for the Bachelor of Science in Mathematics major is provided below. It should be noted that each student's sequence will be unique depending on when the program is started, how many AP or transfer credits are applied and when the desired courses are offered.
| First Year | |||
|---|---|---|---|
| First Semester | Credits | Second Semester | Credits |
| MATH 201 | 1 | MATH 202 | 1 |
| PHYS 211 | 1 | PHYS 212 | 1 |
| 2 | 2 | ||
| Sophomore | |||
| First Semester | Credits | Second Semester | Credits |
| MATH 211 | 1 | MATH 212 | 1 |
| MATH 245 | 1 | MATH 280 | 1 |
| CSCI 203 | 1 | Laboratory science | 1 |
| 3 | 3 | ||
| Junior | |||
| First Semester | Credits | Second Semester | Credits |
| MATH 308 or 320 | 1 | MATH 308 or 320 | 1 |
| Elective in mathematics | 1 | Elective in mathematics | 1 |
| 2 | 2 | ||
| Senior | |||
| First Semester | Credits | Second Semester | Credits |
| Elective in mathematics | 1 | Elective in mathematics | 1 |
| Culminating Experience | 1 | ||
| 1 | 2 | ||
| Total Credits: 17 | |||
Bachelor of Science in Applied Mathematics
The Bachelor of Science in Applied Mathematics major requires nine mathematics courses beyond the introductory year of calculus, a computing course, at least three approved courses in an approved program, and a Culminating Experience. More specifically, there are six required core mathematics courses consisting of:
| Program Requirements | ||
| MATH 211 | Calculus III | 1 |
| MATH 212 | Differential Equations | 1 |
| MATH 245 | Linear Algebra | 1 |
| MATH 280 | Logic, Sets, and Proofs | 1 |
| MATH 303 | Probability | 1 |
| MATH 308 | Real Analysis I | 1 |
| Elective Courses | ||
| Three elective courses in applied mathematics | 3 | |
| A Culminating Experience 5 | ||
| One computing course | 1 | |
| Three approved partner courses | 3 | |
| Total Credits | 13 | |
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The requirement for a Culminating Experience within the major may be satisfied in any of the following ways: (1) taking a full credit 400-level mathematics course; or (2) completing a guided research project, such as an honors thesis, in mathematics, statistics, mathematics education, or applied mathematics. This project should extend beyond one semester and include an initial proposal, a final product, and a public presentation of results; or (3) completing student teaching for secondary certification. The Culminating Experience may be non-credit bearing. The Culminating Experience may not double-count as one of the mathematics electives required in the major. While the Culminating Experience may be met in any of the ways specified above, students earning a Bachelor of Science in Applied Mathematics are strongly encouraged to consider the option of a thesis or research experience integrating the outside coursework. The course for a Culminating Experience may be undertaken in the spring of junior year or the fall or spring of senior year.
The College of Arts & Sciences Core Curriculum disciplinary depth requirements for Bachelor of Science in Applied Mathematics major are satisfied as follows:
- writing within the major in MATH 280 Logic, Sets, and Proofs and MATH 308 Real Analysis I (both W2 courses);
- information literacy in MATH 308 Real Analysis I;
- formal presentation as part of the culminating experience.
Applied Mathematics Electives
| Select three of the following: | 3 | |
| MATH 342 | Topics in Finance or Industry | |
| MATH 343 | Numerical Analysis | |
| MATH 345 | Advanced Linear Algebra | |
| MATH 350 | Partial Differential Equations | |
| MATH 358 | Topics in Operations Research | |
| MATH 362 | Complex Analysis | |
| MATH 409 | Real Analysis II | |
| MATH 416 | Advanced Methods in Mathematical Modeling | |
| Total Credits | 3 | |
Alternative 300 or 400-level mathematics courses could count toward the electives if deemed appropriate by the academic adviser in consultation with the mathematics department chair.
The computing course may be a computer science course at or above the 200 level, or a computing course appropriate to the program of study as determined through consultation with the academic adviser and the mathematics department chair.
Outside Coursework (Partner Courses)
For the purpose of completing a coherent sequence of courses that provide a solid introduction to the discipline, all students must partner with an approved department or program in a discipline that applies mathematics. In this regard, a minimum of three approved courses chosen in consultation with the mathematics department adviser and the outside department or program is required. A partner department/program will usually be chosen from the College of Engineering, the Freeman College of Management, the Division of Social Sciences, or the Division of Natural Sciences. Entering students may declare the intended major in the summer after acceptance to Bucknell, but must consult with the mathematics department and formally declare the outside coursework by the end of their third semester. All other students must consult with the mathematics department at the point of declaring the major and specify the outside coursework. In either case, the mathematics department will consult with the partner department or program to ensure that the coursework is appropriate and can be completed.
A sample sequence for the Bachelor of Science in Applied Mathematics major is provided below. It should be noted that each student's sequence will be unique depending on when the program is started, how many AP or transfer credits are applied, and when the desired courses are offered.
| First Year | |||
|---|---|---|---|
| First Semester | Credits | Second Semester | Credits |
| MATH 201 | 1 | MATH 202 | 1 |
| Computing course | 1 | ||
| 1 | 2 | ||
| Sophomore | |||
| First Semester | Credits | Second Semester | Credits |
| MATH 211 | 1 | MATH 212 | 1 |
| Outside course | 1 | MATH 245 | 1 |
| Outside course | 1 | ||
| 2 | 3 | ||
| Junior | |||
| First Semester | Credits | Second Semester | Credits |
| MATH 280 | 1 | MATH 308 | 1 |
| MATH 303 | 1 | MATH elective | 1 |
| Outside course | 1 | ||
| 3 | 2 | ||
| Senior | |||
| First Semester | Credits | Second Semester | Credits |
| MATH elective | 1 | MATH elective | 1 |
| Culminating experience | |||
| 1 | 1 | ||
| Total Credits: 15 | |||
Bachelor of Science in Statistics
The Bachelor of Science in Statistics major requires 13 mathematics and statistics courses beyond the introductory year of calculus, a computing course, and a Culminating Experience, which may double count with one of the 400-level requirements or electives.
Ten of the 13 mathematics and statistics courses are specified:
| MATH 211 | Calculus III | 1 |
| MATH 216 | Statistics I | 1 |
| MATH 217 | Statistics II | 1 |
| MATH 230 | Data Visualization & Computing | 1 |
| MATH 245 | Linear Algebra | 1 |
| MATH 280 | Logic, Sets, and Proofs | 1 |
| MATH 303 | Probability | 1 |
| MATH 304 | Statistical Inference Theory | 1 |
| MATH 308 | Real Analysis I | 1 |
| MATH 405 | Statistical Modeling | 1 |
| Three elective courses from the following list, two of which must be selected from MATH 306, MATH 354, MATH 407, or MATH 409 | 3 | |
| Bayesian Statistics | ||
| Advanced Linear Algebra | ||
| Modern Data Analysis | ||
| Topics in Operations Research | ||
| Statistical Design of Scientific Studies | ||
| Real Analysis II | ||
| Required Computer Science Course | ||
| Introduction to Computer Science | ||
Total Credits: 16-17
The requirement for a Culminating Experience within the major may be satisfied in any of the following ways: (1) taking one of the courses MATH 405 Statistical Modeling, MATH 407 Statistical Design of Scientific Studies, or MATH 409 Real Analysis II; or (2) completing a guided research project, such as an honors thesis, in statistics or a related area as determined by the department. This project should extend beyond one semester and include an initial proposal, a final product, and a public presentation of results. The Culminating Experience may be non-credit bearing. The Culminating Experience may double count with MATH 405 Statistical Modeling or with one of the 400-level mathematics electives listed for the major. The Culminating Experience may be undertaken in the spring of junior year or the fall or spring of senior year.
The College of Arts & Sciences Core Curriculum disciplinary depth requirements for Bachelor of Science in Statistics major are satisfied as follows:
- writing within the major in MATH 216 Statistics I, MATH 280 Logic, Sets, and Proofs, MATH 308 Real Analysis I (all W2 courses);
- information literacy in MATH 308 Real Analysis I;
- formal presentation as part of the culminating experience.
A sample sequence for the Bachelor of Science in Statistics major is provided below. It should be noted that each student's sequence will be unique, depending on when the program is started, how many AP or transfer credits are applied, and when the desired courses are offered.
| First Year | |||
|---|---|---|---|
| First Semester | Credits | Second Semester | Credits |
| MATH 201 | 1 | MATH 202 | 1 |
| CSCI 203 | 1 | MATH 216 | 1 |
| 2 | 2 | ||
| Sophomore | |||
| First Semester | Credits | Second Semester | Credits |
| MATH 211 | 1 | MATH 230 | 1 |
| MATH 217 | 1 | MATH 280 | 1 |
| 2 | 2 | ||
| Junior | |||
| First Semester | Credits | Second Semester | Credits |
| MATH 245 | 1 | MATH 304 | 1 |
| MATH 303 | 1 | MATH 308 | 1 |
| Culminating Experience1 | 0-1 | ||
| 2 | 2-3 | ||
| Senior | |||
| First Semester | Credits | Second Semester | Credits |
| MATH 405 | 1 | Elective 2 | |
| Elective 1 | MATH 345, 358, 407, or 409 | 1 | |
| MATH 306, 354, 345, or 409 | 1 | Elective 3 | |
| MATH 345, 358, 407, or 409 | 1 | ||
| 2 | 2 | ||
| Total Credits: 16-17 | |||
- 1
Please note the culminating experience may be taken in the spring of the junior year or in the fall or spring of the senior year.
Departmental Honors
Students who complete departmental honors should have a grade point average of at least 3.5 both in their mathematics courses and overall. By the end of their junior year, students in the Bachelor of Arts in Mathematics major or Bachelor of Science in Mathematics major must have completed a total of at least three mathematics courses at the 300- or 400-level, including MATH 308 Real Analysis I or MATH 320 Abstract Algebra I. Students in the Bachelor of Science in Applied Mathematics major must have completed a total of at least three mathematics courses at the 300- or 400- level by the end of their junior year; two such courses suffice if one of them is MATH 308 Real Analysis I. By the end of their junior year students in the Bachelor of Science in Statistics major must have completed a total of at least three mathematics courses at the 300- or 400-level, including MATH 308 Real Analysis I. To be accepted into the Honors Program, a student must satisfy all other requirements as put forth by the University Honors Council. The student must then complete an honors thesis under the adviser’s direction and pass a thesis examination in accordance with the requirements of the University Honors Council. Such students may earn course credit for their thesis work by signing up for at least one half-credit of independent study per semester.
Secondary Teacher Certification
Prospective secondary school teachers (grades 7 – 12) must complete one of the four majors within the department. This certification requires specific mathematics and education courses. Students seeking teacher certification should confer as early as possible with the mathematics and education departments to devise a program of study, which normally will include all requirements for certification in the Commonwealth of Pennsylvania.
Mathematics Minor
A minor in mathematics consists of either:
| MATH courses MATH 211 or above (need credit for at least one of MATH 211, MATH 212, MATH 241, MATH 245, or MATH 280 and at least one course must be at the 300 or 400 level) | 4 | |
| Total Credits | 4 | |
or
| MATH courses MATH 211 or above (need credit for at least one of MATH 211, MATH 212, MATH 241, MATH 245, or MATH 280 and at least two courses must be at the 300 or 400 level) | 3 | |
| Total Credits | 3 | |
All credits counted toward the minor must come from courses taken at Bucknell University.
Mathematics (Statistics) Specific Minor
The minor may be specified as mathematics (statistics) if at least two of the required credits are from among the following list, with no more than one credit from MATH 217 Statistics II and MATH 230 Data Visualization & Computing:
| MATH 217 | Statistics II | 1 |
| MATH 230 | Data Visualization & Computing | 1 |
| MATH 303 | Probability | 1 |
| MATH 304 | Statistical Inference Theory | 1 |
| MATH 306 | Statistical Consulting | 1 |
| MATH 354 | Modern Data Analysis | 1 |
| MATH 405 | Statistical Modeling | 1 |
| MATH 407 | Experimental Design | 1 |
Mathematics (Applied/Modeling Mathematics) Specific Minor
The minor may be specified as mathematics (applied/modeling mathematics) if at least two of the required credits are from among the courses:
| MATH 212 | Differential Equations | 1 |
| MATH 219 | Topics in Applied Mathematics | 1 |
| MATH 342 | Topics in Finance or Industry | 1 |
| MATH 343 | Numerical Analysis | 1 |
| MATH 350 | Partial Differential Equations | 1 |
| MATH 358 | Topics in Operations Research | 1 |
The Department of Mathematics aims to provide both majors and non-majors with the mathematical and statistical knowledge and skills needed to succeed in their chosen field of endeavor. It is also intended that the student experience the elegance and broader impacts of the discipline.
Students earning a BA or BS in Mathematics, a BS in Applied Mathematics, or a BS in Statistics will:
1. Demonstrate knowledge of the principal definitions and theorems in the canon of undergraduate mathematical sciences. (1, 6)
2. Be able to communicate mathematical thought. (1, 7)
3. Apply effectively appropriate quantitative tools and logical modes of thinking to analyze and synthesize information in problem solving situations. (1, 2, 6)
4. Experience the breadth of mathematics and statistics. (2, 9)
Numbers in parentheses reflect related Educational Goals of Bucknell University.
Courses
MATH 112. Introduction to Mathematical Modeling. 1 Credit.
Offered Spring Semester Only; Lecture hours:3
Introduction for the non-specialist to mathematical modeling of real-world phenomena such as voting and networks, using graph theory, probability, and other accessible tools.
MATH 150. Calculus Preparation. .5 Credits.
Offered Fall Semester Only; Lecture hours:3
Exploration of algebraic, exponential, logarithmic and trigonometric functions. Review and use of tools from differential calculus, including limits, to better understand those function classes. Emphasis on modeling and problem-solving techniques. Prerequisite: permission of the instructor.
MATH 192. Topics in Calculus. 1 Credit.
Offered Both Fall and Spring; Lecture hours:3
Elementary calculus and applications taken primarily from economics. Topics include algebraic, exponential, and logarithmic functions, graphs, limits, regular and partial derivatives, constrained optimization, and integration. Not open to students who have MATH 201 credit.
MATH 201. Calculus I. 1 Credit.
Offered Both Fall and Spring; Lecture hours:4
An introduction to the calculus of algebraic, trigonometric and transcendental functions. Interpretation, significance and calculations of derivatives. Applications to geometry, biology, physics, economics, and other subjects. Introduction to the integral, including the Fundamental Theorem of Calculus and substitution. Not open to students who have MATH 192 credit.
MATH 202. Calculus II. 1 Credit.
Offered Both Fall and Spring; Lecture hours:4
Methods of integration including integration by parts, numerical approximations, and improper integrals. Sequences and series, including Taylor series. Polar coordinates, parametric functions, differential equations, and applications. Prerequisite: MATH 201.
MATH 203. Introduction to Mathematical Thought. 1 Credit.
Offered Fall Semester Only; Lecture hours:3,Lab:1.5
An investigation of number, numeration, and operations from the perspective of elementary school teachers and pupils. Open only to B.S. in Education Early Childhood students. Required fieldwork.
MATH 204. Elementary Geometry and Statistics. 1 Credit.
Offered Spring Semester Only; Lecture hours:3,Other:1.5
Investigation of geometric, probabilistic, and statistical concepts related to elementary mathematics and how children learn and make sense of these concepts. Required fieldwork. Prerequisites: MATH 203 or permission of the instructor.
MATH 207. The Teaching of Mathematics in Secondary Schools. 1 Credit.
Offered Fall Semester Only; Lecture hours:3,Other:1.5
Investigation into the components of effective secondary school mathematics instruction, including lesson design/ implementation (curriculum, tasks, discourse, and assessment). Required fieldwork. Prerequisite: EDUC 102 or EDUC 201 or permission of the instructor.
MATH 208. Mathematical Explorations. .5 Credits.
Offered Fall Semester Only; Lecture hours:3
An exploration of topics from pure mathematics, applied mathematics and statistics, illustrating the power and beauty of mathematical reasoning. For students considering a major in mathematics. Corequisites: MATH 201 or MATH 202 or MATH 211 or MATH 212 or MATH 216. Open to first-year students only.
MATH 211. Calculus III. 1 Credit.
Offered Both Fall and Spring; Lecture hours:4
Calculus of vector-valued functions and functions of several variables. Multiple, line, and surface integrals; applications, and extrema. Green's, Stokes' and Divergence Theorems. Prerequisite: MATH 202.
MATH 212. Differential Equations. 1 Credit.
Offered Both Fall and Spring; Lecture hours:3
Basic methods of solving ordinary differential equations. Systems of linear differential equations, Laplace transform, applications and selected topics. Prerequisite: MATH 211. Not open to students who have taken MATH 222.
MATH 216. Statistics I. 1 Credit.
Offered Both Fall and Spring; Lecture hours:3,Other:1
Exploratory data analysis, sampling and experimental designs, sampling distributions and confidence intervals, hypothesis testing, least squares regression and applications. Statistical software is used and a semester long project with real data is undertaken. Not open to students who have MATH 226, MATH 227, ENGR 226 or PSYC 215 credit.
MATH 217. Statistics II. 1 Credit.
Offered Both Fall and Spring; Lecture hours:3,Other:1
Multiple linear regression, logistic regression and ANOVA. Inferential analysis emphasizing applications to a range of disciplines is conducted using statistical software. Prerequisite: MATH 216 or MATH 227 or equivalent. Students who have taken MATH 405 need instructor permission.
MATH 219. Topics in Applied Mathematics. 1 Credit.
Offered Occasionally; Lecture hours:3; Repeatable
Topics such as financial mathematics, mathematical biology, cryptography, social networks, etc. Topic varies by semester. Prerequisite: varies by topic.
MATH 222. Differential Equations for Engineers. .5 Credits.
Offered Spring Semester Only; Lecture hours:3
First order differential equations, second order linear equations, higher order linear equations, numerical approximations. Prerequisite: MATH 211. Open only to civil engineering and environmental engineering students. Not open to students who have MATH 212 credit.
MATH 227. Statistics and Engineering. 1 Credit.
Offered Either Fall or Spring; Lecture hours:3
Probability theory, discrete and continuous random variables, sampling distributions and methods of statistical inference including regression and ANOVA. Software is used. Prerequisite: MATH 202. Open only to engineering students and students in computer science. Not open to students who have MATH 216 or ENGR 226 credit.
MATH 230. Data Visualization & Computing. 1 Credit.
Offered Spring Semester Only; Lecture hours:3
Simulation-based learning for concepts including sampling, sampling distributions, p-values, and confidence levels. Data visualization beyond simple exploratory data analysis techniques. Advanced statistical software will be used. Prerequisite: MATH 216 or MATH 227 or permission of the instructor.
MATH 240. Applied Combinatorics. .5 Credits.
Offered Spring Semester Only; Lecture hours:3
Counting techniques and traversal problems. Students join MATH 241 mid-semester. Pre- or co-requisite: MATH 280. Only for computer science students or students seeking secondary certification. Not open to students who have taken MATH 340.
MATH 241. Discrete Structures. 1 Credit.
Offered Spring Semester Only; Lecture hours:3
Logic, sets; mathematical induction; relations, functions; combinatorics and graph theory. Not open to students with MATH 240, MATH 280 or MATH 340 credit. Prerequisite: MATH 202.
MATH 245. Linear Algebra. 1 Credit.
Offered Both Fall and Spring; Lecture hours:3
Linear equations, matrices, vector spaces, linear transformations, eigenvalues, inner products, Gram-Schmidt algorithm, singular value decomposition. Prerequisite: MATH 202.
MATH 260. Applications to Medicine and Biology. 1 Credit.
Offered Occasionally; Lecture hours:3
Possible topics include using mathematical or statistical modeling to design strategies for controlling epidemics, administering drugs, managing ecosystems, survival analysis, or clinical trials. Topic varies by semester.
MATH 280. Logic, Sets, and Proofs. 1 Credit.
Offered Both Fall and Spring; Lecture hours:3
Logic, sets; proof techniques; relations, functions, sequences and convergence; cardinality. Skills and tools for independent reading, problem solving and exploration. Not open to students with MATH 241 credit. Prerequisite: MATH 211 or MATH 245.
MATH 291. Undergraduate Readings. .5-2 Credits.
Offered Either Fall or Spring; Lecture hours:Varies; Repeatable
Readings and research in special topics at an intermediate level. Prerequisites: permission of the instructor, adviser, and department chair.
MATH 303. Probability. 1 Credit.
Offered Both Fall and Spring; Lecture hours:3
Elementary probability, random variables, moments, central limit theorem, conditional expectation, statistical distributions derived from the normal distribution. Probability simulations and applications from various fields. Prerequisite: MATH 211.
MATH 304. Statistical Inference Theory. 1 Credit.
Offered Both Fall and Spring; Lecture hours:3
Point and interval estimation, Fisher's likelihood theory, hypothesis testing, simulation techniques. R or SAS will be used. Prerequisites: MATH 216 or MATH 227 and MATH 303, or permission of the instructor.
MATH 306. Statistical Consulting. 1 Credit.
Offered Alternating Fall Semester; Lecture hours:3
Client-focused, hands-on, collaborative course where students apply knowledge from prior courses and learn new methods that are versatile for problem solving. Students will communicate findings to clients in both written and oral formats. Advanced statistical software will be used. Prerequisites: MATH 217 and MATH 230, or permission of the instructor.
MATH 308. Real Analysis I. 1 Credit.
Offered Both Fall and Spring; Lecture hours:3
Real numbers and elementary topology of Cartesian spaces, convergence, continuity, differentiation, and history of the development of analysis. Prerequisites: MATH 211, MATH 245, and MATH 280.
MATH 311. Theory of Numbers. 1 Credit.
Offered Alternate Fall or Spring; Lecture hours:3
Classical number theory in an algebraic setting. Topics include unique factorization, diophantine equations, and linear and quadratic congruences. Advanced topics from algebraic or analytic number theory. Prerequisites: MATH 245 and either MATH 241 or MATH 280 or permission of the instructor.
MATH 319. Topics in Advanced Mathematics. 1 Credit.
Offered Alternate Fall or Spring; Lecture hours:3; Repeatable
Special topics, to be selected from algebra, analysis, geometry, statistics, applied mathematics, etc. Prerequisite varies by topic.
MATH 320. Abstract Algebra I. 1 Credit.
Offered Both Fall and Spring; Lecture hours:3
Groups and rings; homomorphisms, isomorphism theorems; history of the development of algebra. Additional selected topics. Prerequisites: MATH 245 and MATH 280.
MATH 333. Topology. 1 Credit.
Offered Alternating Fall Semester; Lecture hours:3
Topological spaces, connectedness, compactness, continuity, separation, and countability axioms. Metric, product, function, and uniform spaces. Prerequisites: MATH 211 and MATH 280, or permission of the instructor.
MATH 335. Geometry. 1 Credit.
Offered Alternating Fall Semester; Lecture hours:3
Historical and axiomatic foundations of geometry. Euclidean and non-Euclidean geometries. Prerequisite: MATH 280 or permission of the instructor.
MATH 340. Combinatorics & Graph Theory. 1 Credit.
Offered Alternating Spring Semester; Lecture hours:3
An introduction to combinatorics and graph theory. Topics include counting techniques, permutations, binomial coefficients, partitions, generating functions, graph traversal, spanning trees, matching theory, planar graphs; additional selected topics. Prerequisite: MATH 280 or permission of the instructor.
MATH 342. Topics in Finance or Industry. 1 Credit.
Offered Alternating Spring Semester; Lecture hours:3
Possible topics include industrial mathematics, financial mathematics, genetic algorithms, simulations, and network analysis. Will also include applications to economics and the writing and presenting of a project. Prerequisites: CSCI 203, MATH 245, and MATH 303 or permission of the instructor.
MATH 343. Numerical Analysis. 1 Credit.
Offered Fall Semester Only; Lecture hours:3,Lab:2
Floating point arithmetic, development of computational algorithms and error estimates for root approximation, interpolation and approximation by polynomials, numerical differentiation and integration, cubic splines, least-squares, linear systems. Lab component. Prerequisites: Two of (MATH 211, MATH 241, MATH 245, MATH 280) and (CSCI 203 or CSCI 204). Crosslisted as MATH 643.
MATH 345. Advanced Linear Algebra. 1 Credit.
Offered Alternate Fall or Spring; Lecture hours:3
Rigorous treatment of linear algebra, including vector spaces, linear independence, span, basis, linear maps, matrices, eigenvalues, eigenvectors, inner products, the spectral theorem (complex and real). Additional topics may include: singular value decomposition, Jordan canonical form, various applications. Prerequisites: MATH 245 and either MATH 280 or permission of the instructor.
MATH 350. Partial Differential Equations. 1 Credit.
Offered Alternate Fall or Spring; Lecture hours:3
Partial Differential Equations (PDEs) including the heat equation, wave equation, and Laplace's equation; existence and uniqueness of solutions to PDEs via the maximum principle and energy methods; method of characteristics; Fourier series and integral transforms; separation of variables; Sturm-Liouville theory and orthogonal expansions. Prerequisites: junior or senior status; MATH 212.
MATH 354. Modern Data Analysis. 1 Credit.
Offered Alternating Fall Semester; Lecture hours:3
Advanced methods in modern data analysis. Topics may include principal component analysis, random forest, clustering and classification, unsupervised learning, splines, longitudinal data analysis, survival analysis, time series, spatial statistics, and nonparametric methods. Prerequisite: MATH 230 and MATH 245, or permission of the instructor.
MATH 358. Topics in Operations Research. 1 Credit.
Offered Spring Semester Only; Lecture hours:3
Mathematical techniques in operations research. Stochastic processes and mathematical optimization. Topics may include Markov chains, queueing theory, simulation, linear programming, non-linear programming, integer programming, network optimization. Methods and applications drawn from various fields. Prerequisite: MATH 227 or MATH 303 or permission of the instructor. Crosslisted as MATH 658.
MATH 362. Complex Analysis. 1 Credit.
Offered Alternating Spring Semester; Lecture hours:3
Limits, analytic functions, integrals including contour integrals. Cauchy's Integral Theorem, entire functions and singularities. Prerequisites: MATH 211 and MATH 280, or permission of the instructor.
MATH 378. Seminar. .5 Credits.
Offered Either Fall or Spring; Lecture hours:2; Repeatable
Seminar based on topics from algebra, analysis, topology, differential equations, statistics, or applied mathematics; topics selected according to demand or interest. Prerequisite: permission of the instructor.
MATH 391. Reading and Research. .5-2 Credits.
Offered Either Fall or Spring; Lecture hours:Varies; Repeatable
Reading and research in various topics for qualified undergraduate students. Prerequisite: permission of the instructor.
MATH 405. Statistical Modeling. 1 Credit.
Offered Fall Semester Only; Lecture hours:3
Theory behind General Linear Models including multiple linear regression and logistic regression. Model diagnostics and remediation. Model selection, multicollinearity. R or SAS will be used. Prerequisites: MATH 245 and MATH 304.
MATH 407. Experimental Design. 1 Credit.
Offered Spring Semester Only; Lecture hours:3
Basic and advanced experimental designs (completely randomized, block, crossed, nested and mixed designs, fractional factorial, incomplete block, etc). Corresponding theory and application of estimation procedures including both frequentist and Bayesian estimation techniques. Advanced statistical software will be used. Prerequisite: MATH 304.
MATH 409. Real Analysis II. 1 Credit.
Offered Alternate Fall or Spring; Lecture hours:3
Continuation of MATH 308. Integration theory and advanced topics in analysis. Prerequisite: MATH 308.
MATH 416. Advanced Methods in Mathematical Modeling. 1 Credit.
Offered Alternate Fall or Spring; Lecture hours:3
A survey of mathematical models grounded in differential equations and methods used to analyze the behavior of their solutions. Topics may include dynamical systems, asymptotics, perturbation methods, variational methods, numerical methods and scientific computing. Prerequisites: MATH 212 and MATH 308 or permission of the instructor. Crosslisted as MATH 616.
MATH 446. Abstract Algebra II. 1 Credit.
Offered Alternate Fall or Spring; Lecture hours:3
Continuation of MATH 320. Advanced topics in group theory including solvable groups, field theory and Galois theory. Prerequisite: MATH 320.
MATH 491. Reading and Research. .5-2 Credits.
Offered Either Fall or Spring; Lecture hours:Varies; Repeatable
Reading and research in various topics for qualified undergraduates or graduate students at a level appropriate for a Culminating Experience. Prerequisite: permission of the instructor, adviser, and department chair.
Faculty
Professors: KB Boomer, M. Lynn Breyfogle, Peter Brooksbank, Thomas Cassidy (Associate Provost for Academic Affairs), Emily B. Dryden, George R. Exner, Peter McNamara, Nathan C. Ryan, Linda B. Smolka, Karl Voss (Dean of the College of Arts & Sciences)
Associate Professors: Kelly A. Bickel, Van T. Cyr, Lara K. Dick, Abby Flynt (Chair), Sharon A. Garthwaite, Owais Gilani, Christina Hamlet, Jeffrey Langford, Kelly McConville (Director for the Dominguez Center for Data Science)
Assistant Professors: Jennifer Berg, Sanjay Dharmavaram, Amy Donner (Teaching), Samuel C. Gutekunst, Keegan Kang, Adam Mair, Aaron Osgood-Zimmerman, Sara Stoudt, Lucas Waddell, Angela Wu
Visiting Assistant Professors: Ángel Chávez, Ryan Reynolds
Postdoctoral Fellow: Manuel Albrizzio