Wednesday, October 3, 2007
First Year
Calculus - 2 subjects, 12 units each
Mathematics is the common language of science and engineering, and calculus is a part of mathematics that is essential for understanding many aspects of the physical world. The two-subject calculus requirement can be fulfilled through various sequences or a combination of subjects and Advanced Placement or Advanced Standing credit, depending on your mathematics background and interests.
The basic 18.01-18.02 calculus sequence is a traditional treatment adapted for MIT students. Both subjects are offered in the fall and spring. The approach is not rigorous; some theorems are proved carefully while others are justified informally.
18.01 Calculus I
Covers differentiation and integration of functions of one variable, with some basic applications. The prerequisites for 18.01 are high school algebra and trigonometry.
18.02 Calculus II
Covers vector and multi-variable calculus. Partial differentiation and multiple integration are studied with applications. Vectors and vector functions are introduced to describe physical notions such as work and force field. Line and surface integrals are covered along with the theorems of Green, Gauss, and Stokes, which are fundamental in many problems of physics and engineering. A variant of 18.02 is described below. It is only offered in the fall term.
18.022 Calculus II
Covers the material of 18.02, but at greater depth. Additional material is included in geometry, vector fields, and linear algebra.
Advanced Placement and Credit
A score of 4 or 5 on the Calculus BC exam gives you credit for 18.01. You may also receive credit for 18.01 by transferring credit from a comparable college course taken elsewhere, or by passing an advanced standing exam. If you have credit for 18.01, you may begin with 18.02 or 18.022. If you have some calculus experience but not enough to get 18.01 credit, or wish to review the material even if you were given 18.01 credit, consider the 18.01A-18.02A sequence.
18.01A-18.02A Calculus I and II
18.01A Fall only (six weeks) 18.02A Fall, plus IAP or Spring
This sequence, intended for students who have had a full year of high school calculus, begins with 18.01A, a six-week review of one-variable calculus, emphasizing integration techniques and applications, polar coordinates, improper integrals, and infinite series. Prerequisite is a score of 4 or 5 on the Advanced Placement Calculus AB exam or a passing grade on the first half of the 18.01 Advanced Standing Exam, covering differentiation and elementary integration. Most students completing 18.01A will continue directly into 18.02A, in which the remaining weeks of the fall term will be devoted to the material in the first half of Calculus II. 18.02A will be taught at the same pace as 18.02. Students will then complete the second half of Calculus II either during Independent Activities Period (IAP) in January or during the first half of the spring term.
Credit Notes: Students opting for 18.01A-18.02A will register for both 18.01A and 18.02A in the fall term, and for 18.02A in IAP or the spring term. They will receive 12 units of credit upon completion of each subject, for a total of 24 units. Only 12 units (six for 18.01A and six for 18.02A) will be counted toward the fall term credit limit (54 units). Depending on when the second half of Calculus II is taken, six units will be applied toward the Independent Activities Period credit limit (12 units) or the spring term credit limit (57 units).
Students with 18.01 credit who decide to take 18.01A to review their calculus will lose the 12 units of 18.01 credit and instead receive three units of general elective credit.
18.014-18.024 Calculus with Theory
18.014 Fall only
18.024 Spring only
This version of the calculus sequence is intended for students with strong interest and ability in mathematics. Emphasis is placed on careful definitions of the concepts traditionally treated in calculus, and on mathematically rigorous proofs of the basic theorems of the subject. Students choosing 18.014 should already be familiar with the computational aspects of single-variable calculus. These aspects will, however, be reviewed when they arise during the term. The text by Apostol is used.
Credit Note: Students with 18.01 credit who decide to take 18.014 will lose the 12 units of 18.01 credit and instead receive nine units of general elective credit.
Advice for Choosing Your Fall Term Calculus Subject
-
If you have had less than a full year of calculus in high school, enroll in 18.01.
-
If you have had a full year of calculus but do not have 18.01 credit, take the 18.01 Advanced Standing Examination. Passing the first part gives eligibility for 18.01A. Passing both parts gives 18.01 credit.
-
If you have 18.01 credit, you may choose between 18.02 and 18.022. If you wish a review, you may take 18.01A.
-
If you are especially interested in mathematics and have some prior calculus experience, consider 18.014.
All calculus lectures are scheduled at the same time to facilitate switching to another sequence if the one you choose isn't suitable. However, with the exception of 18.01 and 18.01A, each subject sequence uses a different book, so some catching up would be necessary.
Choosing Subjects
The question as to what math subject to take next is a question that students ask frequently. It is a question to which there is no pat answer. The answer would be simple if the math curriculum were organized so that one simply marched through it in lockstep—18.01, 18,02, 18.03, 18.04, 18.05, and so on indefinitely. But it is not that easy.
Take a look at the chart provided. (Note: this chart is a large graphic.) This chart exhibits all the undergraduate subjects beyond 18.03 offered by the Mathematics Department at MIT, organized into eight different areas (by columns), and arranged into four levels of difficulty (by rows) with Level I being easiest. We strongly advise you not to tackle a subject on one level until you have completed at least one subject on the preceding level (the arrows indicate prerequisites). First-year graduate subjects in the various fields are listed at the bottom. Subjects enclosed in square brackets involve both adjacent fields.
As you can see, the organization of the curriculum is certainly not a simple linear one. Nevertheless, there are some general guidelines concerning what math subject is appropriate for a student with given preparation and interests. Guidlines for first year students are listed on the calculus page. Guidelines for students who have completed 18.03 or for majors and non-majors ready for higher level courses are also available.
If you have completed 18.03, any subject listed on the first row of the chart is suitable as a next mathematics subject. Of these, the subjects 18.04 (Complex Variables) and 18.06 (Linear Algebra) are taken most often closely followed by 18.05 (Probability and Statistics). (In fact, 18.05 and 18.06 require only 18.02 as a prerequisite.) Each of these subjects is useful for students majoring in a wide variety of disciplines. Each of these subjects is also suitable for students who plan to major in mathematics. For such students, or for those who simply wish to select a somewhat more demanding subject, there are further possibilities:
When you get beyond the beginning subjects in any of the listed areas of mathematics, the chart can give you some guidance as to an appropriate next subject. You will need to be sure you have the necessary prerequisites. You should also be aware of the level of difficulty and/or abstraction of the subject. Now, let us turn to a description of these subjects themselves: |
| Analysis | Algebra | Geometry and Topology | ||
| Logic | Continuous Applied Math | Discrete Applied Math | ||
| Theoretical Computer Science | Probability and Statistics | Seminars | ||
| top | ||||
ANALYSIS Real Analysis (18.100, 18.101, 18.103, 18.152) deals with real-valued functions of real variables, as in calculus, but with complete rigor and considerable abstraction. 18.100 is concerned with functions of a single variable and their derivatives and integrals, in the context of metric spaces. It is a prerequisite for many other subjects. (Some bright sophomores do well in this subject, on the other hand, it is probably more frequently dropped than any other math subject at MIT. It helps if the student has already had some experience with proofs.) There is a version of 18.100 (called "Option A") that is somewhat slower paced and less abstract. 18.101 treats functions of several variables; topics include derivatives and integrals in n dimensions, and the n-dimensional version of Stokes' theorem (involving differential forms rather than vector fields). 18.103 treats the Lebesgue integral (which is different from the familiar Riemann integral of calculus) and Fourier analysis. (18.125 also treats the Lebesgue integral, but much more abstractly; it is a graduate subject.) 18.152 is a mathematical treatment of partial differential equations; it is a logical sequel to 18.03 or 18.034. Complex Analysis (18.04, 18.112, 18.115, 18.075) deals with complex-valued functions of a complex variable. Although the concepts studied may seem familiar—derivatives, integrals, and the like—the results are remarkably different from those in real analysis. The applications are many and varied; the so-called "imaginary" numbers have important real-life applications to physics and engineering. 18.04 is an elementary introduction to the subject, taken by many EE majors. 18.112 is a deeper and more extensive treatment, mathematical rigor is not stressed however. 18.115 is a theoretical, theorem-proving treatment, it is a graduate subject, which is taken by many advanced undergraduates. Overlapping 18.100 and 18.112 and 18.103 is the "Advanced Calculus for Engineers" sequence 18.075-18.076. Although designed with engineering students in mind, it is taken by a few other students as well. It covers topics in both real and complex analysis that are useful in applications. Both 18.04 and 18.075 may not be taken for credit. ALGEBRA Linear Algebra (18.06, 18.700) deals with solving systems of linear equations, both concretely using matrix algebra and more abstractly using vector spaces and linear transformations. Its subject matter is basic in mathematics, and everyone should have some knowledge of it, 18.06 emphasizes the concrete approach using matrices, while 18.700 is more abstract and proof oriented. (Linear algebra is also treated briefly in 18.701.) Modern Algebra (18.703, 18.701-18.702) is the study of certain abstractly defined systems (called groups, rings, and fields) whose properties generalize those of integers, polynomials, and matrices. Using these concepts one can prove, for instance, that the general angle cannot be trisected by a Euclidean construction, and that there is no formula like the quadratic formula for solving polynomial equations of the 5th degree. There are modem applications to such subjects as coding theory and cryptography. 18.703 is a standard introduction to the subject. 18.701-18.702 is a more intensive high-level sequence, the student should have some experience with proofs (as in 18.100 or 18.700) before taking this subject. GEOMETRY AND TOPOLOGY Topology (18.901 ) deals with quite general objects called "topological spaces" which are more general than the metric spaces of analysis and the surfaces and manifolds of geometry. It studies such familiar notions as compactness and connectedness, and then goes on to such topics as metrization theorems and product spaces. Writing proofs is emphasized. Differential Geometry (18.950) is an introduction to modem geometry. The basic objects of study are smooth curves and surfaces in Euclidean space. Topics include curvature and geodesics, and their relation to the nature of the curve or surface. LOGIC Logic forms the very foundation of mathematics. One studies how mathematical statements are formulated, what it means for them to be true, what a proof is, and whether all true statements in a mathematical system can be proven within the confines of that system. Either 18.510 or 18.511 constitutes a basic introduction. The first halves of these two courses are the same; but the second half of 18.510 is formal set theory and the second half of 18.511 is recursion theory. 18.423J is a subject that explores the connections between logic and computer science, it is jointly offered with Course 6. CONTINUOUS APPLIED MATHEMATICS Continuous applied mathematics deals most commonly with the mathematics of classical physics and continuum mechanics. 18.311 is an elementary introduction-, it builds on the basics of calculus and differential equations to provide insight into more difficult problems and to give the flavor of the methods used in applied mathematics. 18.303 is the basic high-level subject in this area. It concentrates on the partial differential equations of physics and applied mathematics, along with their applications and methods of solutions. Nonlinear Dynamics (18.353-18.354) deals with understanding the differential equations of science and engineering. 18.353 studies maps and ordinary differential equations, explaining the qualitative properties of solutions, and conditions under which they can become chaotic. 18.354 concerns the mathematical principles underlying continuum systems. Fundamental ideas include averaging, singular perturbations, instability, and turbulence. Numerical Analysis (18.330) deals with finding efficient methods of determining numerical solutions to problems generated by engineering and science. Sample problems include approximating an integral or finding roots of an algebraic equation. The calculations are usually done with the aid of a computer or calculator. DISCRETE APPLIED MATHEMATICS 18.310 is an elementary introduction to this area- calculus is the only prerequisite, but linear algebra might be helpful. Topics vary, but have included linear programming. coding theory, scheduling, sorting, and game theory. It is skewed toward applications to real world problems. 18.062J is somewhat more elementary, it treats those aspects of mathematics that are basic for computer science. Combinatorics (18.312, 18.314) 18.314 deals With such topics as graph theory, enumeration problems, and sorting; there are applications to computer science. This is the basic introduction to combinatorics at MIT, though it has few prerequisites, it is distinctly not elementary. 18.312 deals with the applications of modem algebra to combinatorics; it is a bit more advanced. Combinatorial Optimization(18.433) gives a thorough treatment of linear programming, which is one of the basic tools of operations research and is heavily used in business and industry. THEORETICAL COMPUTER SCIENCE This subject deals with the mathematical aspects of the field of computer science. Theory of Computation (18.400J, 18.404J) treats the theoretical foundations underlying modem computers, topics include Turing machines, automata, and complexity. 18.400J is an introduction to the subject, oriented toward applications; 18.404J provides a more extensive and theoretical treatment of the same material. Algorithms (18.410J, 18.421) treats the design and analysis of efficient problem solving algorithms. 18.410J is an applications-oriented introduction; 18.421 deals more specifically with algorithms for solving problems from classical algebra and number theory. PROBABILITY AND STATISTICS Probability and Statistics constitute one of the most widely used fields of mathematics, being of great importance in the experimental sciences. 18.05 is an elementary introduction to both areas; it is taken primarily by non-math majors. Probability (18.313, 18.440) deals with measuring the likelihood of the occurrence of a given event, or series of events. Both 18.313 and 18.440 cover basic probability; they are equivalent for prerequisite purposes. 18.440 is the standard introduction. 18.313 is an alternative version; it is taught in a lecture-recitation format and is somewhat more demanding mathematically. Statistics (18.441, 18.443) deals with analyzing of data and drawing inferences from the results. 18.441 is the standard introduction. 18.443 is an alternative version that is oriented more towards the applications of statistics and less toward theory. Both require a background in probability SEMINARS The upper-level seminars in mathematics are designed for students who plan to do graduate work in mathematics. In such a seminar the student studies a particular area of mathematics under the guidance of a faculty member, learning to read mathematics independently and to organize and present the results. Topics covered in the seminars in analysis 18.104), logic (18.504), and algebra (18.704), vary from year to year. The seminar in topology (18.904) is an introduction to algebraic topology, in which one uses tools of algebra to study problems of topology, by studying the fundamental group of a topological space. |
Undergraduate Study - Degree Options
There are four undergraduate programs in mathematics. The first three (General Mathematics, Applied Mathematics and Theoretical Mathematics) lead to the degree Bachelor of Science in Mathematics, and the fourth (Mathematics with Computer Science) to the degree Bachelor of Science in Mathematics with Computer Science. The requirements for these programs are given in the following sections.
The breadth of careers envisioned by Mathematics Majors has led to the creation of a number of subjects with similar content. The following limitation applies to all four degree options: Subjects taken to satisfy the Mathematics degree requirements must not have essentially similar content. Specifically, you may count at most one of the subjects from each of the following lists.
- 18.06 or 18.700 (Linear Algebra)
- 18.702 or 18.703 (Algebra)
- 18.04 or 18.075 or 18.112 (Complex Variables)
- 18.05 or 18.440 or 6.041 (Probability)
- 18.304 or 18.316 (Combinatorics)
- 18.400J or 18.404J (Computation)
Textbooks
| Course | Book | Author | ISBN |
|---|---|---|---|
| 18.01 | Calculus with Analytic Geometry, 2nd edit | simmons | 0070576424 |
| 18.014 | Calculus, Volume 1, Second Edition | Apostol | 0471000051 |
| 18.01A | Calculus with Analytic Geometry, 2nd edit | Simmons | 0070576424 |
| 18.02 | Multivariable Calculus, 6th edition* | Edwards & Penney | 0130339679 |
| 18.022 | Vector Calculus, 3rd edition; packaged with Student Solutions Manual | Colley | 013-187013-0 |
| 18.023 | Calculus an Introduction to Applied Mathematics | Greenspan & Benney | 0962699810 |
| 18.03 | Elementary Differential Equations with Boundary Value Problems, 5th edit.; Bundled with Or | Edwards & Penney | Bundle 013150 |
| 18.06 | Introduction to Linear Algebra, 3rd edition* | Strang | 0961408898 |
| 18.075 | (Advanced Calculus for Applications, 2nd edition) | Hildebrand | 0130111899 |
| 18.085 | Computational Science and Engineering | Strang | tba |
| 18.100A | Introduction to Analysis | Mattuck | 0130811327 |
| 18.100B | Principles of Mathematical Analysis, 3rd edit | Rudin | 007054235x |
| Principles of Mathematical Analysis, 3rd edit | Rudin | 007054235x | |
| Principles of Mathematical Analysis, 3rd edit | Rudin | 007054235x | |
| 18.100C | Principles of Mathematical Analysis, 3rd edit | Rudin | 007054235x |
| 18.101 | Analysis on Manifolds | Munkres | 0201315963 |
| Calculus on Manifolds | Spivak | 0805390219 | |
| 18.102 | Introduction to Hilbert Spaces With Applications | Debnath & Mikusinski | 0122084381 |
| 18.112 | Complex Analysis | Ahlfors | 0070006571 |
| 18.117 | Partial Differential Equations in Several Complex Variable | Chen and Shaw | 0821829610 |
| 18.152 | (Partial Differential Equations: An Introduction) | Strauss | 0471548685 |
| 18.177 | Brownian Motion and Stochastic Calculus | Karatzas & Shreve | 0387976558 |
| 18.303 | (Linear Partial Differential Equations for Scientists and Engineers, 4th edition)* | Myint-U & Debnath | 0817643931 |
| Partial Differential Equations of Mathematical Physics and Integral Equations | Guenther & Lee | 0486688895 | |
| 18.304 | (Proofs From the Book, 3rd edition)* | Aigner & Ziegler | 3540404600 |
| 18.305 | Advanced Analytic Methods in Applied Mathematics, Science, and Engineering | Cheng | 0975862510 |
| 18.314 | (A Walk Through Combinatorics, 2nd edition) | Bona | 9812568859 |
| 18.315 | Enumerative Combinatorics, Vol. 1, 2nd edit | Stanley | 0521663512 |
| 18.335 | Numerical Linear Algebra | Trefethen and Bau | 0898713617 |
| 18.385 | (Nonlinear Systems)* | Drazin | 0521404894 |
| (Practical Numerical Algorithms for Chaotic Systems)* | Parker & Chua | 0387966897 | |
| (Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edit.) | Wiggins | 0387001778 | |
| (Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields)* | Guckenheimer & Holmes | 0387908196 | |
| (Order within Chaos)* | Berge, Pomeau, Vidal | 0471849677 | |
| (Nonlinear Dynamics and Chaos) | Strogatz | 0738204536 | |
| (Introduction to Celestial Mechanics)* | McCuskey | 0486646874 | |
| (Nonlinear Ordinary Differential Equations)* | Jordan &Smith | 0198565623 | |
| 18.404 | Introduction to the Theory of Computation, 2nd edition | Sipser | 0534950973 |
| 18.440 | A First Course in Probability, 7th edition | Ross | 0131856626 |
| 18.443 | Probability and Statistics, 3rd edition | Degroot & Schervish | 0201524880 |
| 18.465 | Modern Applied Statistics with S, 4th edit | Venables & Ripley | 0387954570 |
| 18.511 | Mathematical Logic, 2nd edition | Ebbinhaus, Flum &Thomas | 0387942580 |
| 18.515 | Mathematical Logic, 2nd edition | Ebbinhaus, Flum &Thomas | 0387942580 |
| 18.700 | Linear Algebra | Jacob | Copytech |
| 18.701 | Algebra | Artin | 0130047635 |
| 18.704 | (An Introduction to Grobner Bases)* | Adams & Loustaunau | 0821838040 |
| (Using Algebraic Geometry, 2nd Edition)* | Cox, Little and O'Shea | 0387207333 | |
| (Computational Algebraic Geometry)* | Schenck | 0521536502 | |
| Ideals, Varieties and Algorithms* | Cox, Little and O'Shea | 0387356509 | |
| 18.705 | Undergraduate Commutative Algebra* | Reid | 0521458897 |
| (Commutative Algebra)* | Eisenbud | 0387942696 | |
| Introduction to Commutative Algebra* | Atiyah & Macdonald | 0201407515 | |
| 18.755 | Differential Geometry, Lie Groups and Symmetric Spaces | Helgason | 0821828487 |
| 18.781 | (An Introduction to the Theory of Numbers, 5th edition)* | Hardy | 0198531710 |
| An Introduction to the Theory of Numbers, 5th edition* | Niven, Zuckerman & Montgomery | 0471625469 | |
| 18.784 | Quantum Calculus* | Kac & Cheung | 0387953418 |
| 18.901 | Topology, 2nd edition | Munkres | 0131816292 |
| 18.904 | (Algebraic Topology: An Introduction) | Massey | 0387902716 |
| 18.905 | (Algebraic Topology) | Hatcher | 0521795400 |
| 18.917 | (Unstable Modules Over The Steenrod Algebra and Sullivan's Fixed Point Set Conjecture) | Schwartz | 0226742032 |
| 18.950 | (Differential Geometry of Curves and Surfaces)* | do Carmo | 0132125897 |
| Differential Geometry: Curves-Surfaces-Manifolds, 2nd edit.* | Kuehnel | 0821839888 | |
| 18.965 | (Introduction to Smooth Manifolds) | Lee | 0387954481 |
| (Foundations of Differentiable Manifolds and Lie Groups) | Warner | 0387908943 | |
| (Morse Theory) | Milnor | 0691080089 | |
| 18.A11 | Euler: The Master of Us All | Dunham | 0883853280 |
| 18.S11 | Number Theory for Beginners | Weil | Copytech |
Undergraduate Study
Calculus - 2 subjects, 12 units each
Mathematics is the common language of science and engineering, and calculus is a part of mathematics that is essential for understanding many aspects of the physical world. The two-subject calculus requirement can be fulfilled through various sequences or a combination of subjects and Advanced Placement or Advanced Standing credit, depending on your mathematics background and interests.
The basic 18.01-18.02 calculus sequence is a traditional treatment adapted for MIT students. Both subjects are offered in the fall and spring. The approach is not rigorous; some theorems are proved carefully while others are justified informally.
18.01 Calculus I
Covers differentiation and integration of functions of one variable, with some basic applications. The prerequisites for 18.01 are high school algebra and trigonometry.
18.02 Calculus II
Covers vector and multi-variable calculus. Partial differentiation and multiple integration are studied with applications. Vectors and vector functions are introduced to describe physical notions such as work and force field. Line and surface integrals are covered along with the theorems of Green, Gauss, and Stokes, which are fundamental in many problems of physics and engineering. A variant of 18.02 is described below. It is only offered in the fall term.
18.022 Calculus II
Covers the material of 18.02, but at greater depth. Additional material is included in geometry, vector fields, and linear algebra.
Advanced Placement and Credit
A score of 4 or 5 on the Calculus BC exam gives you credit for 18.01. You may also receive credit for 18.01 by transferring credit from a comparable college course taken elsewhere, or by passing an advanced standing exam. If you have credit for 18.01, you may begin with 18.02 or 18.022. If you have some calculus experience but not enough to get 18.01 credit, or wish to review the material even if you were given 18.01 credit, consider the 18.01A-18.02A sequence.
18.01A-18.02A Calculus I and II
18.01A Fall only (six weeks) 18.02A Fall, plus IAP or Spring
This sequence, intended for students who have had a full year of high school calculus, begins with 18.01A, a six-week review of one-variable calculus, emphasizing integration techniques and applications, polar coordinates, improper integrals, and infinite series. Prerequisite is a score of 4 or 5 on the Advanced Placement Calculus AB exam or a passing grade on the first half of the 18.01 Advanced Standing Exam, covering differentiation and elementary integration. Most students completing 18.01A will continue directly into 18.02A, in which the remaining weeks of the fall term will be devoted to the material in the first half of Calculus II. 18.02A will be taught at the same pace as 18.02. Students will then complete the second half of Calculus II either during Independent Activities Period (IAP) in January or during the first half of the spring term.
Credit Notes: Students opting for 18.01A-18.02A will register for both 18.01A and 18.02A in the fall term, and for 18.02A in IAP or the spring term. They will receive 12 units of credit upon completion of each subject, for a total of 24 units. Only 12 units (six for 18.01A and six for 18.02A) will be counted toward the fall term credit limit (54 units). Depending on when the second half of Calculus II is taken, six units will be applied toward the Independent Activities Period credit limit (12 units) or the spring term credit limit (57 units).
Students with 18.01 credit who decide to take 18.01A to review their calculus will lose the 12 units of 18.01 credit and instead receive three units of general elective credit.
18.014-18.024 Calculus with Theory
18.014 Fall only
18.024 Spring only
This version of the calculus sequence is intended for students with strong interest and ability in mathematics. Emphasis is placed on careful definitions of the concepts traditionally treated in calculus, and on mathematically rigorous proofs of the basic theorems of the subject. Students choosing 18.014 should already be familiar with the computational aspects of single-variable calculus. These aspects will, however, be reviewed when they arise during the term. The text by Apostol is used.
Credit Note: Students with 18.01 credit who decide to take 18.014 will lose the 12 units of 18.01 credit and instead receive nine units of general elective credit.
Advice for Choosing Your Fall Term Calculus Subject
-
If you have had less than a full year of calculus in high school, enroll in 18.01.
-
If you have had a full year of calculus but do not have 18.01 credit, take the 18.01 Advanced Standing Examination. Passing the first part gives eligibility for 18.01A. Passing both parts gives 18.01 credit.
-
If you have 18.01 credit, you may choose between 18.02 and 18.022. If you wish a review, you may take 18.01A.
-
If you are especially interested in mathematics and have some prior calculus experience, consider 18.014.
All calculus lectures are scheduled at the same time to facilitate switching to another sequence if the one you choose isn't suitable. However, with the exception of 18.01 and 18.01A, each subject sequence uses a different book, so some catching up would be necessary.
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