Introductory Courses

Calculus stands as one of the great intellectual achievements of the last millennium, developed by Newton and Leibniz to understand motion, growth, and change. Math Ma, the first-semester in a full-year sequence, introduces students to that achievement by focusing on one of its central ideas: how differential calculus describes rates of change. Throughout, students will see mathematical ideas at work in concrete problems drawn from the physical sciences, life sciences, economics, and everyday contexts. A central theme of differential calculus is understanding, describing, and calculating rates of change. Students will develop and analyze models that provide opportunities for deep exploration of linear, quadratic, polynomial, rational, exponential, and logarithmic functions, and their use in representing real-world phenomena. Students will learn to interpret derivatives, both graphically and numerically, and connect derivatives to the shape and behavior of graphs. They will use calculus techniques—including product, quotient, and chain rules—to reason deeply about models they’ve built, solve optimization problems, and describe function behavior. Throughout the semester, students will engage in high-level reasoning using algebra to justify their conclusions, interpret situations, test ideas, and make sense of unfamiliar problems. The goal of the course is a robust and deeply connected understanding of the ideas within differential calculus. Conceptual understanding is emphasized throughout the curriculum to provide students with a strong foundation on which to build toward more and more advanced mathematics. This course is appropriate for students with and without previous calculus experience. Techniques from high school algebra are used right away and students who have taken a break from mathematics can expect to spend extra time reviewing them.

Course Notes:

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). This course, when taken together with Mathematics LS, can satisfy a number of different requirements for students interested in the life sciences or students on the pre-med track. See Math LS for more information.

Course Notes:

The first time you enroll in any introductory math course (Math Ma through Math 22a), you are required to take a Math Verification Exam. Your results may determine which introductory course(s) you are eligible to take. For more information please go to this website (https://canvas.harvard.edu/courses/168499).

Course Notes:

Math Ma is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). For information about how to register for this course and to rank your time preferences, please see the Canvas site. There will be required workshops Tuesdays. Workshop will be scheduled the first week of class. Information will be available via Canvas. Exams for this course will occur throughout the semester on Thursdays in the block from 6:00 - 9:00 pm. Consult Canvas for more details on the exact Thursdays. The course will have a mandatory information meeting on the morning of the first day of the semester. Information will be available via Canvas.

Course Notes:

Midterms will be scheduled on various Thursdays during the block 6:00 PM - 9:00 PM. You will sign up for a "Quiz Section" to block this time on your schedule. If there is an unavoidable academic conflict, please email Sarah Chin explaining your conflict and why it is unavoidable. She will arrange an alternative time for you.

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Calculus stands as one of the great intellectual achievements of the last millennium, developed by Newton and Leibniz to understand motion, growth, and change. Math Ma, the first-semester in a full-year sequence, introduces students to that achievement by focusing on one of its central ideas: how differential calculus describes rates of change. Throughout, students will see mathematical ideas at work in concrete problems drawn from the physical sciences, life sciences, economics, and everyday contexts. A central theme of differential calculus is understanding, describing, and calculating rates of change. Students will develop and analyze models that provide opportunities for deep exploration of linear, quadratic, polynomial, rational, exponential, and logarithmic functions, and their use in representing real-world phenomena. Students will learn to interpret derivatives, both graphically and numerically, and connect derivatives to the shape and behavior of graphs. They will use calculus techniques—including product, quotient, and chain rules—to reason deeply about models they’ve built, solve optimization problems, and describe function behavior. Throughout the semester, students will engage in high-level reasoning using algebra to justify their conclusions, interpret situations, test ideas, and make sense of unfamiliar problems. The goal of the course is a robust and deeply connected understanding of the ideas within differential calculus. Conceptual understanding is emphasized throughout the curriculum to provide students with a strong foundation on which to build toward more and more advanced mathematics. This course is appropriate for students with and without previous calculus experience. Techniques from high school algebra are used right away and students who have taken a break from mathematics can expect to spend extra time reviewing them.

Course Notes:

After Math Ma5, students may take Math Mb (just like Math Ma students). Math Ma5 and Math Mb can then be followed by Mathematics 1b. Mathematics Ma5 and Mb together cover all the material in Mathematics 1a (and more). This course, when taken together with Mathematics LS, can satisfy a number of different requirements for students interested in the life sciences or students on the pre-med track. See Math LS for more information.

Course Notes:

The first time you enroll in any introductory math course (Math Ma through Math 22a), you are required to take a Math Verification Exam. Your results may determine which introductory course(s) you are eligible to take. For more information please go to this website (https://canvas.harvard.edu/courses/168499).

Course Notes:

Math Ma5 is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). For information about how to register for this course and to rank your time preferences, please see the Canvas site. There will be required workshops Tuesdays. Workshop will be scheduled the first week of class. Information will be available via Canvas. Exams for this course will occur throughout the semester on Thursdays in the block from 6:00 - 9:00 pm. Consult Canvas for more details on the exact Thursdays. The course will have a mandatory information meeting on the morning of the first day of the semester. Information will be available via Canvas.

Course Notes:

Midterms will be scheduled on various Thursdays during the block 6:00 PM - 9:00 PM. You will sign up for a "Quiz Section" to block this time on your schedule. If there is an unavoidable academic conflict, please email Sarah Chin explaining your conflict and why it is unavoidable. She will arrange an alternative time for you.

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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. There will be required workshops Tuesdays.

Requirements:

Prerequisite: Mathematics MA or Mathematics MA5

Course Notes:

Math Mb is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). For information about how to register for this course and to rank your time preferences, please see the Canvas site. There will be required workshops Tuesdays. Workshop will be scheduled the first week of class. Information will be available via Canvas. Exams for this course will occur throughout the semester on Thursdays in the block from 6:00 - 9:00 pm. Consult Canvas for more details on the exact Thursdays. The course will have a mandatory information meeting on the morning of the first day of the semester. Information will be available via Canvas.

Course Notes:

Midterms will be scheduled on various Thursdays during the block 6:00 PM - 9:00 PM. You will sign up for a "Quiz Section" to block this time on your schedule.If there is an unavoidable academic conflict, please email Sarah Chin explaining your conflict and why it is unavoidable. She will arrange an alternative time for you.

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Calculus stands as one of the great intellectual achievements of the last millennium, developed by Newton and Leibniz to understand motion, growth, and change. This single-variable course introduces you to that achievement by focusing on these central ideas: how differential calculus describes rates of change, how integral calculus describes accumulation, and how the Fundamental Theorem of Calculus connects them. Throughout, you will see these ideas at work in concrete problems drawn from the physical sciences, life sciences, economics, and everyday contexts. A central theme of the course is understanding, describing, and calculating rates of change. You will learn to interpret derivatives graphically and numerically, connect derivatives to the shape and behavior of graphs, and use derivative techniques—including product, quotient, and chain rules, implicit and logarithmic differentiation—to solve optimization and related rates problems in context. In the second part of the course, attention shifts from rates to accumulation. You will be introduced to the definite integral as a precise way to describe accumulated change over time—mathematically, a way of “adding up pieces” such as small changes, areas, or contributions to a total. Throughout the semester, you will use algebraic reasoning—together with graphical, numerical, and symbolic representations of functions—to justify your conclusions, interpret situations, test ideas, and make sense of unfamiliar problems.

Recommended Prep:

Strong precalculus skills are essential for success in this course. If you are advised to take Math Ma, that recommendation indicates that your precalculus foundation needs strengthening, and you should take the recommendation seriously.

Requirements:

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

Course Notes:

The first time you enroll in any introductory math course (Math Ma through Math 22a), you are required to take a Math Verification Exam. Your results may determine which introductory course(s) you are eligible to take. For more information please go to this website: https://canvas.harvard.edu/courses/168499.

Course Notes:

Math 1a is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). For information about how to register for this course and to rank your time preferences, please see the Canvas site. Exams for this course will ocur throughout the semester on Thursdays in the block from 6:00 - 9:00 pm. Consult Canvas for more details on the exact Thursdays. The course will have a mandatory information meeting on the morning of the first day of the semester. Information will be available via Canvas.

Course Notes:

Midterms will be scheduled on various Thursdays during the block 6:00 PM - 9:00 PM. You will sign up for a "Quiz Section" to block this time on your schedule. If there is an unavoidable academic conflict, please email Sarah Chin explaining your conflict and why it is unavoidable. She will arrange an alternative time for you.

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Math 1b is a continuation of single-variable calculus that deepens your fluency in the language of modern mathematics—the language in which ideas across the sciences and engineering are expressed and understood. Focusing on integration, infinite series, and differential equations, the course emphasizes modeling real-world phenomena and understanding change in the physical, life, and social sciences. A central theme is successive approximation: finding approximate solutions when exact ones are difficult or impossible, improving those approximations, and understanding and controlling error. By the end of the course, you will have both a strong conceptual grasp of these ideas and the practical skills to apply them in a wide range of scientific an quantitative contexts.

Recommended Prep:

Mathematics 1a or an equivlent background is required for success in Math 1b.

Requirements:

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

Course notes:

The first time you enroll in any introductory math course (Math Ma through Math 22a), you are required to take a Math Verification Exam. Your results may determine which introductory course(s) you are eligible to take. For more information please go to this website: https://canvas.harvard.edu/courses/168499.

Course notes:

Math 1b is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). For information about how to register for this course and to rank your time preferences, please see the Canvas site. Exams for this course will occur throughout the semester on Thursdays in the block from 6:00 - 9:00 pm. Consult Canvas for more details on the exact Thursdays. The course will have a mandatory information meeting on the morning of the first day of the semester. Information will be available via Canvas.

Course notes:

Midterms will be scheduled on various Thursdays during the block 6:00 PM - 9:00 PM. You will sign up for a "Quiz Section" to block this time on your schedule. If there is an unavoidable academic conflict, please email Sarah Chin explaining your conflict and why it is unavoidable. She will arrange an alternative time for you.

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Math 1b is a continuation of single-variable calculus that deepens your fluency in the language of modern mathematics—the language in which ideas across the sciences and engineering are expressed and understood. Focusing on integration, infinite series, and differential equations, the course emphasizes modeling real-world phenomena and understanding change in the physical, life, and social sciences.A central theme is successive approximation: finding approximate solutions when exact ones are difficult or impossible, improving those approximations, and understanding and controlling error. By the end of the course, you will have both a strong conceptual grasp of these ideas and the practical skills to apply them in a wide range of scientific and quantitative contexts.

Recommended Prep:

Mathematics 1a or an equivalent background is required for success in Math 1b.

Requirements:

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

Course Notes:

The first time you enroll in any introductory math course (Math Ma through Math 22a), you are required to take a Math Verification Exam. Your results may determine which introductory course(s) you are eligible to take. For more information please go to this website: https://canvas.harvard.edu/courses/168499.

Course Notes:

Math 1b is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). For information about how to register for this course and to rank your time preferences, please see the Canvas site. Exams for this course will occur throughout the semester on Thursdays in the block from 6:00 - 9:00 pm. Consult Canvas for more details on the exact Thursdays. The course will have a mandatory information meeting on the morning of the first day of the semester. Information will be available via Canvas.

Course Notes:

Midterms will be scheduled on various Thursdays during the block 6:00 PM - 9:00 PM. You will sign up for a "Quiz Section" to block this time on your schedule.If there is an unavoidable academic conflict, please email Sarah Chin explaining your conflict and why it is unavoidable. She will arrange an alternative time for you.

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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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Science relies on understanding quantitative relationships in many different contexts, and many of the most useful relationships are functions of several variables. For this reason, multivariable calculus is a foundational subject with wide-ranging applications in physics, engineering, economics, data science, machine learning, and the life sciences. In this course, we develop geometric reasoning to build intuition about functions of multiple variables. You will learn to describe and visualize curves, surfaces, and solid regions in space, and to see how familiar ideas from single-variable calculus—such as limits, derivatives, and integrals—extend to these new settings.You will work with vectors, lines, and planes; explore partial derivatives, gradients, and optimization; and study vector fields that model phenomena such as electricity and magnetism, flow, and circulation. These concepts culminate in the central theorems of vector calculus—Green’s Theorem, Stokes’s Theorem, and the Divergence Theorem—which reveal deep connections between local behavior and global structure. Throughout, the course emphasizes geometric intuition, visualization, problem solving, quantitative reasoning, and a strong conceptual understanding of the structures underlying multivariable calculus.

Recommended Prep:

Mathematics 1b, or an equivalent background, is essential preparation for Math 21a. Skipping Math 1b can be detrimental to your academic progress. If your concentration requires Math 21a or Math 21b, you may in fact need the skills, concepts, and ways of reasoning developed in Math 1b. Check with a concentration advisor before skipping Math 1b, as doing so is generally not advisable.

Requirements:

Anti-requisite: Cannot be taken for credit if Math 18A or Math 22B already complete.

Course Notes:

The first time you enroll in any introductory math course (Math Ma through Math 22a), you are required to take a Math Verification Exam. Your results may determine which introductory course(s) you are eligible to take. For more information please go to this website: https://canvas.harvard.

Course Notes:

Math 21a is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). For information about how to register for this course and to rank your time preferences, please see the Canvas site. The course will have a mandatory information meeting on the morning of the first day of the semester. Information will be available via Canvas.

Course Notes:

Midterms will be scheduled on various Thursdays during the block 6:00 PM - 9:00 PM. You will sign up for a "Quiz Section" to block this time on your schedule. If there is an unavoidable academic conflict, please email Sarah Chin explaining your conflict and why it is unavoidable. She will arrange an alternative time for you.

:

Science relies on understanding quantitative relationships in many different contexts, and many of the most useful relationships are functions of several variables. For this reason, multivariable calculus is a foundational subject with wide-ranging applications in physics, engineering, economics, data science, machine learning, and the life sciences. In this course, we develop geometric reasoning to build intuition about functions of multiple variables. You will learn to describe and visualize curves, surfaces, and solid regions in space, and to see how familiar ideas from single-variable calculus—such as limits, derivatives, and integrals—extend to these new settings. You will work with vectors, lines, and planes; explore partial derivatives, gradients, and optimization; and study vector fields that model phenomena such as electricity and magnetism, flow, and circulation. These concepts culminate in the central theorems of vector calculus—Green’s Theorem, Stokes’s Theorem, and the Divergence Theorem—which reveal deep connections between local behavior and global structure. Throughout, the course emphasizes geometric intuition, visualization, problem solving, quantitative reasoning, and a strong conceptual understanding of the structures underlying multivariable calculus.

Recommended Prep:

Mathematics 1b, or an equivalent background, is essential preparation for Math 21a. Skipping Math 1b can be detrimental to your academic progress. If your concentration requires Math 21a or Math 21b, you may in fact need the skills, concepts, and ways of reasoning developed in Math 1b. Check with a concentration advisor before skipping Math 1b, as doing so is generally not advisable.

Requirements:

Anti-requisite: Cannot be taken for credit if Math 18A or Math 22B already complete.

Course Notes:

The first time you enroll in any introductory math course (Math Ma through Math 22a), you are required to take a Math Verification Exam. Your results may determine which introductory course(s) you are eligible to take. For more information please go to this website: https://canvas.harvard.edu/courses/168499.

Course Notes:

Math 21a is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). For information about how to register for this course and to rank your time preferences, please see the Canvas site. The course will have a mandatory information meeting on the morning of the first day of the semester. Information will be available via Canvas.

Course Notes:

Midterms will be scheduled on various Thursdays during the block 6:00 PM - 9:00 PM. You will sign up for a "Quiz Section" to block this time on your schedule. If there is an unavoidable academic conflict, please email Sarah Chin explaining your conflict and why it is unavoidable. She will arrange an alternative time for you.

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Linear algebra is one of the most widely used areas of mathematics; it has applications in fields as varied as computer science, economics, engineering, epidemiology, ecology, physics, psychology, archaeology and statistics. In linear algebra, we study linear transformations, an important group of functions that play a role in the various applications mentioned above. We’ll start from a very concrete perspective, that of solving linear systems, but we’ll quickly see that we can also adopt a more geometric perspective, which is often useful. Linear transformations enable us to deal with higher-dimensional phenomena as well as vast amounts of data. As we progress through the course, the level of abstraction will increase. This is key, because it allows us to generalize our knowledge to broader and broader contexts. We’ll see how linear algebra can be applied to dynamical systems and differential equations, which model processes throughout the natural and social sciences, and to Fourier series, which are used in engineering and the sciences to analyze waves, signals, and other periodic phenomena.

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. If you plan on taking both Math 21a and Math 21b, we highly recommend taking Math 21a first.

Requirements:

Anti-requisite: Cannot be taken for credit if you have passed MATH 22A or AM 22A

Course Notes:

The first time you enroll in any introductory math course (Math Ma through Math 22a), you are required to take a Math Verification Exam. Your results may determine which introductory course(s) you are eligible to take. For more information please go to this website: https://canvas.harvard.edu/courses/168499

Course Notes:

Math 21b is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). For information about how to register for this course and to rank your time preferences, please see the Canvas site. The course will have a mandatory information meeting on the morning of the first day of the semester.

Course Notes:

Midterms will be scheduled on various Thursdays during the block 6:00 PM - 9:00 PM. You will sign up for a "Quiz Section" to block this time on your schedule. If there is an unavoidable academic conflict, please email Sarah Chin explaining your conflict and why it is unavoidable. She will arrange an alternative time for you.

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Linear algebra is one of the most widely used areas of mathematics; it has applications in fields as varied as computer science, economics, engineering, epidemiology, ecology, physics, psychology, archaeology and statistics. In linear algebra, we study linear transformations, an important group of functions that play a role in the various applications mentioned above. We’ll start from a very concrete perspective, that of solving linear systems, but we’ll quickly see that we can also adopt a more geometric perspective, which is often useful. Linear transformations enable us to deal with higher-dimensional phenomena as well as vast amounts of data. As we progress through the course, the level of abstraction will increase. This is key, because it allows us to generalize our knowledge to broader and broader contexts. We’ll see how linear algebra can be applied to dynamical systems and differential equations, which model processes throughout the natural and social sciences, and to Fourier series, which are used in engineering and the sciences to analyze waves, signals, and other periodic phenomena.

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. If you plan on taking both Math 21a and Math 21b, we highly recommend taking Math 21a first.

Requirements:

Anti-requisite: Cannot be taken for credit if you have passed MATH 22A or AM 22A

Course Notes:

The first time you enroll in any introductory math course (Math Ma through Math 22a), you are required to take a Math Verification Exam. Your results may determine which introductory course(s) you are eligible to take. For more information please go to this website: https://canvas.harvard.edu/courses/168499

Course Notes:

Math 21b is taught in small sections throughout the day on a Monday/Wednesday/Friday schedule (9:00-10:15 am, 10:30-11:45 am, 12-1:15 pm, 1:30-2:45 pm, and 3:00-4:15 pm with sufficient enrollment). For information about how to register for this course and to rank your time preferences, please see the Canvas site. The course will have a mandatory information meeting on the morning of the first day of the semester.

Course Notes:

Midterms will be scheduled on various Thursdays during the block 6:00 PM - 9:00 PM. You will sign up for a "Quiz Section" to block this time on your schedule. If there is an unavoidable academic conflict, please email Sarah Chin explaining your conflict and why it is unavoidable. She will arrange an alternative time for you.

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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).

Course Requirements:

Anti-requisite: Cannot be taken for credit if you have passed Math 21B, Math 25A, Math 121, or AM 22A

Course Notes:

The first time you enroll in any introductory math course (Math Ma through Math 22a), you are required to take a Math Verification Exam. Your results may determine which introductory course(s) you are eligible to take. For more information please go to this website: https://canvas.harvard.edu/courses/168499.

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Math 22b is a proof-based introduction to multivariable calculus for students interested in mathematical sciences. It covers the same topics as Math 21a, but with greater rigor and with an emphasis on reading, writing, and understanding mathematical proofs. The workload for Math 22b is designed to be comparable to Math 21a. Students should have previously taken a course that teaches an introduction to proofs, for example, Math 22a; and students should also have experience with linear algebra. In addition to a focus on proofs, Mat 22b uses more linear algebra concepts than Math 21a in developing multivariable calculus.

Requirements:

Anti-requisite: Cannot be taken for credit if Math 18A, Math 21A, or AM 22B already complete.

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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.

Requirements:

Anti-requisite: Cannot be taken for credit if Math 18A, Math 21A, Math 22B, Math 101, Math 112, or AM 22B already complete.

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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, 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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