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Math at ESG - Fall 2004

ESG offers the first-year MIT mathematics subjects, with most of the variations. One of ESG's emphases is on individualized instruction, and often this is reflected in students' interest in our Independent Study options in 18.01, 18.02 and 18.03. Our experience has been that incoming MIT students have quite diverse backgrounds in mathematics, and our emphasis on small groups and the possibility of Independent Study allow a finer sorting of students according to their capabilities. The Fall 2003 and Spring 2004 listings are also available.

Students entering ESG in the Fall term have of course been through the same process as all first-year students, and have had some options narrowed by the Advanced Standing/Advanced Placement process. Specifically, each student knows the subject in which to "start,'' identified by a subject number. Within a given subject, however, are many possible starting places. Students always do best when they begin at the appropriate place, so that material that is already known well need not be repeated, and students taking one of the accelerated variations of a subject need not have to catch up at the beginning. In the following list, the subject numbers in parentheses are links to MIT's online catalogue; ESG has the same criteria in place for determining which subject is appropriate. For the Independent Study options, where the subject material is online, links are given to those home pages, but anyone looking at these pages should know that the material will be revised over the summer. Still, you will get an idea of what to expect.

Questions? Contact one of the staff members listed below, or the instructors for the specific subjects.

ESG Math Staff, Fall 2004:

• Dr. John B. Lewis (jlewis@math.mit.edu)
• Jerry Orloff (jorloff@mit.edu)
• Craig Watkins (watko@mit.edu)

For a condensed, two-page printable version of this page (no color graphics, and you have to use your imagination for any animation), here's MATH at ESG - Printable.

Calculus (18.01)

This is the "standard'' version of single-variable calculus, for those who have had little or no previous exposure to calculus, and so are ready to begin a fascinating subject. An old Syllabus is online.

Contact: Craig Watkins

Calculus - Advanced (18.01A)

Anyone wishing to take an accelerated version of 18.01 must have taken and passed the first half of the Mathematics Department's 18.01 Advanced Standing exam, covering differentiation and elementary integration. (If you've followed that link, you know that more information will be available later in the summer.)

Contact: Nirav Shah; Nirav's 18.01A syllabus from last year is online. (This year's is coming!)

Calculus - Independent Study

(Students completing the Independent Study sequence would receive credit for (18.01).

Students electing this option would have more choices of where to start, depending on their background. Although we call it "Independent Study'', students with similar backgrounds and interests are encouraged to work together, usually with an instructor. The 18.01IS materials are online.

The fact that the above website is in the "18.01A'' directory indicates that Independent Study was a forerunner of 18.01A. Anyone wishing to start 18.01IS at an advanced level must either have taken and passed the first half of the Mathematics Department's 18.01 Advanced Standing exam (see 18.01A above) or ESG's own 18.01IS Advanced Placement test. Warning: We have more time to put into grading these, and this is reflected in the nature of the questions. Figure it out.

To see the sorts of things we'll be looking at throughout the term (and you can make a rough judgment of how much of the subject you already know), take a look at the 18.01IS preview problems, Xdvi or PDF. (Hard copies should be generated from the PDF version.) This year's problems have an added twist, in that they investigate the use of calculus in applied poetry. Check it out to see what, if anything, this means.

Contact: Craig Watkins

Calculus with Applications (18.013A)

The (18.013A-18.023A) sequence entails an intensive use of resources not available to ESG.

Calculus with Theory (18.014)

Unfortunately, it is not likely to be offered at ESG this term.

Calculus (18.02)

The "standard'' multivariable calculus, an interesting and essential subject. At ESG, we offer several different variations of 18.02 (but NOT 18.022, and 18.024 only in the Spring). A very good background in single-variable calculus is assumed; students who are not confident of their 18.01-level preparation sometimes find that a review of some of the 18.01IS units is in order. Some review problems (which all 18.02 students should be able to do) are available, either Xdvi or PDF. A Syllabus from Fall 2001 is available (PDF only) for John's group(s), and John's first problem set from last year is still online, PDF only.

Contact: John Lewis.

Calculus - Independent Study (18.02)

This course is also known at ESG as "18.02IS''. Historically, this variation has not been the chosen option for first-term students, but the possibility exists. Students completing 18.01 early are welcome to continue in 18.02IS in the first term. There are two versions of this option, depending on the text used (details upon request). The material is online at 18.02IS - Simmons or 18.02IS - Edwards & Penney.

Contact: Craig Watkins

Calculus with Applications (18.023)

A really fun subject, but one which requires a very good background in single-variable calculus, including series. The material for ESG's version of 18.023 is online at 18.023 - ESG. Students wishing to take 18.023 at ESG must demonstrate adequate preparation by taking and passing a Qualifying Exam on Registration Day (Tuesday September 7); the qualifying exams from the past five years are available through the above link, and interested students are encourage to try these tests as part of preparing for 18.023 at ESG.

The Math department offering (18.023A) depends on daily lectures during IAP, an intensive effort that ESG cannot duplicate.

Contact: Craig Watkins

Differential Equations (18.03)

A popular and important subject. Take a look at those prerequisites; indeed, some variation of 18.02 is a prerequisite. At ESG, we do not waive this requirement; those wishing to take 18.03 and 18.02 simultaneously will have to go elsewhere.

A set of last term's introductory "Warm-up Problems'' is online, Xdvi or PDF; one of these problems refers to Leibniz' Rule.

Last Fall's syllabus in online at 18.03-ESG, Fall 2001, PDF or Xdvi .

Contact: Craig Watkins or Jerry Orloff.

Differential Equations - Independent Study (18.03)

Known at ESG as 18.03IS, this has proven to be quite successful and popular over the years. 18.03IS requires use of Athena software to model nonlinear systems, and perhaps even more, depending on the students' desire. The materials (currently being updated, mainly to reflect the enhanced capabilities for numerical methods) are online at 18.03IS.

A set of introductory "Warm-up Problems'' is online, Xdvi or PDF; one of these problems refers to Leibniz' Rule.

Contact: Craig Watkins

Linear Algebra (18.06)

This course will be offered only if there is sufficient demand and we the staff available to teach the subject. (As of August 14, neither criteria is close to being operative.) For an idea of how Linear Algebra as offered at ESG differs from the typical offering, take a look at the Spring 2000 announcement offering the availability of this subject.

Math Software at ESG

ESG has been a bit ahead of the rest of the Institute in terms of requiring the use of Athena software for certain analytic and graphing purposes. The extent to which students will take advantage of this aspect of ESG will depend on the subject and instructor. To get a taste of what we have done in the past, see Using Maple for ESG Subjects (currently being revised to reflect the new default release on Athena). Shown here is an example of what we can do:

(see Animated Hyperboloids for an explanation of what's going on).

Questions? Contact Jeremy Orloff, John Lewis or Craig Watkins.

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