# Introductory Courses

*Reshma Menon*

2022 Fall (4 Credits)

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Schedule: **
TBD

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

The study of functions and their rates of change. Fundamental ideas of calculus are introduced early and used to provide a framework for the study of mathematical modeling involving algebraic, exponential, and logarithmic functions. Thorough understanding of differential calculus promoted by year long reinforcement. Applications to biology and economics emphasized according to the interests of our students.

- Course Notes:
- This is a lecture course taught in small sections. This course, when taken together with Mathematics Mb, can be followed by Mathematics 1b. Mathematics Ma and Mb together cover all the material in Mathematics 1a (and more).

:

*Matthew Cavallo*

2023 Spring (4 Credits)

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Schedule: **
TBD

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

Continued investigation of functions and differential calculus through modeling; an introduction to integration with applications; an introduction to differential equations. Solid preparation for Mathematics 1b.

- Course Notes:
- This is a lecture course taught in small sections. This course, when taken together with Mathematics Ma, can be followed by Mathematics 1b. Mathematics Ma and Mathematics Mb together cover all the material in Mathematics 1a (and more).

- Requirements:
- Prerequisite: Mathematics MA

:

*Brendan Kelly*

2022 Fall (4 Credits)

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Schedule: **
MWF 0130 PM - 0245 PM

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Instructor Permissions: **
Instructor

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Enrollment Cap: **
50

This course develops a portable toolkit of quantitative skills that supports students’ strategic thinking. At the center of the course is a set of case studies that require comprehensive quantitative analysis to properly diagnose and address the broad range of problems presented. After taking this course, students’ strategic thinking will be bolstered by the ability to develop mathematical models, apply core ideas from differential and integral calculus and statistics to solve problems in economics and social science, and make use of spreadsheets and the R statistical package to carry out data analysis. Each analytical tool comes to life in an authentic application. The course focuses not just on how to carry out the analysis, but how to communicate results to a non-mathematical audience in simple functional language. This course should be seen as an applied alternative for Math Ma/Math Mb or Math 1a for students interested in Economics and the Social Sciences. Students completing Math Qa and Math Qb will satisfy the Math 1a requirement for the Economics Concentration. Completing both Math Qa and Math Qb can count as a course toward the Mathematics Concentration. After completing Math Qa and Math Qb, students’ next math course would normally be Math 1b, but the course serves as great preparation for other quantitative courses such as STAT 104, EC 50, and GOV 50 .

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*Brendan Kelly*

2023 Spring (4 Credits)

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Schedule: **
MWF 01:30 PM - 02:45 PM

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

This course develops a portable toolkit of quantitative skills that supports students’ strategic thinking. At the center of the course is a set of case studies from a broad range of organizations that require comprehensive quantitative analysis to properly diagnose and address the problems presented. After taking this course, students’ strategic thinking will be bolstered by the ability to develop mathematical models, apply core ideas from differential and integral calculus to problems in economics and social science, and make use of the R statistical package to carry out data analysis. Each analytical tool comes to life in an authentic application. The course focuses not just on how to carry out the analysis, but how to communicate results to a non-mathematical audience in simple functional language. This course should be seen as an applied alternative for Math Ma/Math Mb or Math 1a for students interested in Economics and the Social Sciences. Students completing Math Qa and Math Qb will satisfy the Math 1a requirement for the Economics Concentration. Completing both Math Qa and Math Qb can count as a course toward the Mathematics Concentration. After completing Math Qa and Math Qb, students’ next math course could be Math 1b or Math 18a, depending on students’ interests.

:

*Dylan Quintana*

2022 Fall (4 Credits)

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Schedule: **
TBD

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

The development of calculus by Newton and Leibniz ranks among the greatest achievements of the past millennium. This course will help you see why by introducing: how differential calculus treats rates of change; how integral calculus treats accumulation; and how the fundamental theorem of calculus links the two. These ideas will be applied to problems from many other disciplines.

- Course Notes:
- In the fall, Math 1a is taught in small sections. In the spring, Math 1a is taught in a larger lecture format. Mathematics Ma and Mb together cover all of the material in Mathematics 1a (and more).

- Recommended Prep:
- A solid background in precalculus.

- Requirements:
- Anti-requisite: cannot be taken for credit if MATH S-1AB already complete.

:

*Michael Nathanson*

2023 Spring (4 Credits)

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Schedule: **
MWF 01:30 PM - 02:45 PM

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

The development of calculus by Newton and Leibniz ranks among the greatest achievements of the past millennium. This course will help you see why by introducing: how differential calculus treats rates of change; how integral calculus treats accumulation; and how the fundamental theorem of calculus links the two. These ideas will be applied to problems from many other disciplines.

- Course Notes:
- In the fall, Math 1a is taught in small sections. In the spring, Math 1a is taught in a larger lecture format. Mathematics Ma and Mb together cover all of the material in Mathematics 1a (and more).

- Recommended Prep:
- A solid background in precalculus.

- Requirements:
- Anti-requisite: cannot be taken for credit if MATH S-1AB already complete.

:

*Cliff Taubes*

2022 Fall (4 Credits)

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Schedule: **
TBD

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

Speaking the language of modern mathematics requires fluency with the topics of this course: infinite series, integration, and differential equations. Model practical situations using integrals and differential equations. Learn how to represent interesting functions using series and find qualitative, numerical, and analytic ways of studying differential equations. Develop both conceptual understanding and the ability to apply it.

- Course Notes:
- This is a lecture taught in small sections.

- Recommended Prep:
- Mathematics 1a or Ma and Mb; or 5 on the AB advanced placement test; or an equivalent background in mathematics.

- Requirements:
- Anti-requisite: cannot be taken for credit if MATH S-1AB already complete.

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*Amadeus Martin*

2023 Spring (4 Credits)

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Schedule: **
TBD

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

Speaking the language of modern mathematics requires fluency with the topics of this course: infinite series, integration, and differential equations. Model practical situations using integrals and differential equations. Learn how to represent interesting functions using series and find qualitative, numerical, and analytic ways of studying differential equations. Develop both conceptual understanding and the ability to apply it.

- Course Notes:
- This is a lecture taught in small sections.

- Recommended Prep:
- Mathematics 1a or Ma and Mb; or 5 on the AB advanced placement test; or an equivalent background in mathematics.

- Requirements:
- Anti-requisite: cannot be taken for credit if MATH S-1AB already complete.

:

*Philip Wood*

2022 Fall (4 Credits)

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Schedule: **
MWF 12:00 PM - 1:15 PM

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

Focus on concepts and techniques of multivariable calculus most useful to those studying the social sciences, particularly economics: functions of several variables; partial derivatives; linear approximation; multiple integrals; directional derivatives and the gradient; constrained and unconstrained optimization, including the method of Lagrange multipliers. Covers topics from Mathematics 21a most useful to social sciences.

- Course Notes:
- Mathematics 21b can be taken before or after Mathematics 18. Examples draw primarily from economics and the social sciences, though Mathematics 18 may be useful to students in certain natural sciences. Students whose main interests lie in the physical sciences, mathematics, or engineering should consider Math 21a or Applied Math 22a.

- Recommended Prep:
- Mathematics 1b or equivalent, or a 5 on the BC Advanced Placement Examination in Mathematics.

- Requirements:
- Anti-requisite: Not to be taken in addition to Mathematics 21a or Applied Mathematics 22a.

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*John Cain*

2022 Fall (4 Credits)

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Schedule: **
MWF 10:30 AM - 11:45 AM

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

Considers the construction and analysis of mathematical models that arise in the life sciences, ecology and environmental life science. Introduces mathematics that include multivariable calculus, differential equations in one or more variables, vectors, matrices, and linear and non-linear dynamical systems. Taught via examples from current literature (both good and bad).

- Course Notes:
- This course is recommended over Math 21a for those planning to concentrate on the life sciences and ESPP. Can be taken with or without Mathematics 21a,b. Students with interests in the social sciences and economics might consider Mathematics 18. This course can be taken before or after Mathematics 18.

- Recommended Prep:
- A course in one variable calculus preferably at the level of Mathematics 1b.

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*Tyler Bongers*

2023 Spring (4 Credits)

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Schedule: **
MWF 09:00 AM - 10:15 AM

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

Probability, statistics and linear algebra with applications to life sciences, chemistry, environmental sciences, economics and social sciences. Students will learn to use computing software to perform relevant calculations on data sets coming from these areas of study. Linear algebra includes matrices, eigenvalues, eigenvectors, determinants, and applications to probability, statistics, dynamical systems. Basic probability and statistics are introduced, as are standard models, techniques, and their uses including the central limit theorem, Markov chains, curve fitting, regression, and pattern analysis.

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*Janet Chen*

2022 Fall (4 Credits)

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Schedule: **
TBD

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

To see how calculus applies in practical situations described by more than one variable, we study integration over curves, surfaces, and solid regions using different coordinate systems; parameterization of curves and surfaces; vectors, lines, and planes; partial derivatives and the gradient; constrained and unconstrained optimization; divergence and curl of vector fields; and the Green’s, Stokes’s, and Divergence Theorems.

- Course Notes:
- This course is taught in small sections. May not be taken for credit by students who have passed Applied Mathematics 22a.

- Recommended Prep:
- Mathematics 1b or an equivalent background in mathematics.

- Requirements:
- Anti-requisite: Not to be taken in addition to AM 22b.

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*Roderic Guigo Corominas*

2023 Spring (4 Credits)

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Schedule: **
TBD

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

To see how calculus applies in practical situations described by more than one variable, we study integration over curves, surfaces, and solid regions using different coordinate systems; parameterization of curves and surfaces; vectors, lines, and planes; partial derivatives and the gradient; constrained and unconstrained optimization; divergence and curl of vector fields; and the Green’s, Stokes’s, and Divergence Theorems.

- Course Notes:
- This course is taught in small sections. May not be taken for credit by students who have passed Applied Mathematics 22a.

- Recommended Prep:
- Mathematics 1b or an equivalent background in mathematics.

- Requirements:
- Anti-requisite: Not to be taken in addition to AM 22b

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*Tyler Bongers*

2022 Fall (4 Credits)

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Schedule: **
TBD

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

Matrices provide the algebraic structure for solving myriad problems across the sciences. We study matrices and related topics such as linear transformations and linear spaces, determinants, eigenvalues, and eigenvectors. Applications include dynamical systems, ordinary and partial differential equations, and an introduction to Fourier series.

- Course Notes:
- This is a lecture taught in small sections. May not be taken by students who have passed Applied Mathematics 21b.

- Recommended Prep:
- Mathematics 1b or an equivalent background in mathematics. Mathematics 21a is commonly taken before Mathematics 21b, but is not a prerequisite, although familiarity with partial derivatives is useful.

- Requirements:
- Anti-requisite: Not to be taken in addition to AM 22a.

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*Jill Guerra*

2023 Spring (4 Credits)

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Schedule: **
TBD

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

Matrices provide the algebraic structure for solving myriad problems across the sciences. We study matrices and related topics such as linear transformations and linear spaces, determinants, eigenvalues, and eigenvectors. Applications include dynamical systems, ordinary and partial differential equations, and an introduction to Fourier series.

- Course Notes:
- This is a lecture taught in small sections. May not be taken by students who have passed Applied Mathematics 21b.

- Recommended Prep:
- Mathematics 1b or an equivalent background in mathematics. Mathematics 21a is commonly taken before Mathematics 21b, but is not a prerequisite, although familiarity with partial derivatives is useful.

- Requirements:
- Anti-requisite: Not to be taken in addition to AM 22a.

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*Dusty Grundmeier*

2022 Fall (4 Credits)

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Schedule: **
MWF 12:00 PM - 01:15 PM

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

Mathematics 22 covers multivariable calculus and linear algebra for students interested in mathematical sciences. It covers the same topics as Mathematics 21, but does so with more rigor. Students are taught techniques of proof and mathematical reasoning. The workload and content is comparable with the Mathematics 21 sequence. But unlike the latter, the linear algebra and calculus are more interlinked. The content of Math 22a is mostly aligned with Math 21b (linear algebra), and the content of Math 22b is mostly aligned with Math 21a (multivariable calculus).

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*Dusty Grundmeier*

2023 Spring (4 Credits)

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Schedule: **
MWF 12:00 PM - 01:15 PM

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

A continuation of Mathematics 22a.

:

*John Cain*

2022 Fall (4 Credits)

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Schedule: **
MWF 09:00 AM - 10:15 AM

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

A rigorous treatment of linear algebra. Topics include: Construction of number systems; fields, vector spaces and linear transformations; eigenvalues and eigenvectors, determinants and inner products. Metric spaces, compactness and connectedness.

- Course Notes:
- Expect to spend a lot of time doing mathematics.

- Recommended Prep:
- 5 on the Calculus BC Advanced Placement Examination and some familiarity with writing proofs, or the equivalent as determined by the instructor.

:

*John Cain*

2023 Spring (4 Credits)

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Schedule: **
MWF 09:00 AM - 10:15 AM

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Instructor Permissions: **
None

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Enrollment Cap: **
n/a

A rigorous treatment of basic analysis. Topics include: convergence, continuity, differentiation, the Riemann integral, uniform convergence, the Stone-Weierstrass theorem, Fourier series, differentiation in several variables. Additional topics, including the classical results of vector calculus in two and three dimensions, as time allows.

- Course Notes:
- Expect to spend a lot time doing mathematics.

- Requirements:
- Prerequisite: Mathematics 25A OR Mathematics 55A.

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*Joseph D. Harris*

2022 Fall (4 Credits)

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Schedule: **
MWF 10:30 AM - 11:45 AM

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Instructor Permission: **
Instructor

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Enrollment Cap: **
n/a

A rigorous introduction to abstract algebra, including group theory and linear algebra. This course covers the equivalent of Mathematics 25a and Mathematics 122, and prepares students for Mathematics 123 and other advanced courses in number theory and algebra. (A course in analysis such as Mathematics 25b or 55b is recommended for Spring semester.)

- Course Notes:
- Mathematics 55a is an intensive course for students who are comfortable with abstract mathematics. (Students without this background will gain it and learn the material from Math 55a,b in other courses by continuing into the Mathematics Concentration as sophomores.) Students can switch between Mathematics 55a and either Mathematics 25a, 23a, 22a, 21a during the first three weeks without penalty.

- Recommended Prep:
- Familiarity with proofs and abstract reasoning; and commitment to a fast-moving course.

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*Joseph D. Harris*

2023 Spring (4 Credits)

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Schedule: **
MWF 10:30 AM - 11:45 AM

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Instructor Permissions: **
Instructor

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Enrollment Cap: **
n/a

A rigorous introduction to real and complex analysis. This course covers the equivalent of Mathematics 25b and Mathematics 113, and prepares students for Mathematics 114 and other advanced courses in analysis.

- Course Notes:
- Mathematics 55b is an intensive course for students having significant experience with abstract mathematics.

- Requirements:
- Prerequisite: Mathematics 55A.

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