Introductory Courses

There will be required workshops Tuesdays. 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

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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.

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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.

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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 course is 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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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 course is 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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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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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 in 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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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 22b.

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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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 22b.

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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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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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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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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A continuation of Mathematics 22a.

Requirements:

Pre-Requisite: Students must complete Math 22A prior to enrolling in this course.

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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.

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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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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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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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