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118 is actually a blending of material in 120 and 222, squeezed into one semester, and directed toward the social sciences, particularly economics. It is a quick way to get the "math you need" for those subjects, but at a certain price in depth of coverage. In particular, 118 does not usually cover the integration theorems (Green, Gauss and Stokes).
120 is "multivariable calculus" and 250 is "vector calculus". What is the difference? 120 focuses on situations where "multi" really means 2 or 3 -- that means it leans heavily on geometric intuition, and is strongly grounded in geometric applications in engineering and the sciences. 250 generalizes this to the setting of n dimensions, or variables, where n can be 3, 10, or 450,000. In order to do this, linear algebra must be brought in as a tool to manage the computations and to clarify what is conceptually going on -- that's why 222 or 225 is a prerequisite to 250. The theorems of Green, Gauss and Stokes, the beautiful integral equalities that are the capstone of 120, are generalized in 250 to a single master theorem (still called Stokes' theorem) which applies in any dimension. Don't think that 450,000 dimensions means the subject is not practical: any large system, such as the economy or the weather, can easily involve that many variables.
Both courses cover linear algebra, but 222 focuses more on computational techniques and applications, while 225 emphasizes mathematical proofs and a more conceptual approach.
230(a and b) is a two term course with an integrated treatment of linear algebra and vector calculus. This is a demanding but rewarding course for students with a very strong interest and background. 250 is the third semester of the sequence 120-225-250 (or 120-222-250), and covers just the vector calculus.
The department's placement exam is a tool for you to gauge which of 112, 115 or 120 is suitable for you. The raw scores are not enough -- together with personalized advice at the placement session we can help you find the right course, and place into an available section. More about placement here
After reading the descriptions in the YCPS and this web page, contact the course instructor. If still uncertain contact the DUS.
It is permitted to "drop down" from a more advanced course to a less advanced course in a sequence: from 115 to 112, 120 to 115, 230 to 222 or to 120, and a few others. This can be done until the first midterm (sometimes a bit afterwards), but you must consult with the instructors of BOTH courses to manage the transfer smoothly. Thus we encourage you to be ambitious, but realistic, about your course choices.
See here for a list of textbooks used in recent semesters. This semester may be different; for up to date information contact the department registrar.
This is not recommended, but if your previous background is sufficiently strong you may try to obtain permission from the instructor.
This is not a good idea unless your background is quite strong.
The gateways to the core areas of mathematics are provided by these courses: Real Analysis (300 or 301), Algebra (350) and Complex Analysis (310). They are beautiful subjects and every math major is strongly encouraged to take them and continue upwards with the sequences that they begin. Starting with the class of 2012, all math majors are required to take courses in 2 out of 3 of the core areas. Intensive majors must take all three.
Undergraduate research opportunities, and opportunities for guided independent study, do exist, depending on your interest and that of available faculty. During the summer the department organizes REU opportunities for interested students. The department also awards the John Alan Lewis prize each spring, which provides stipends for independent work during the summer. Contact the DUS, or check the website, for more information.
Yes, if you have the appropriate background. You should obtain the approval of the instructor and of the Director of Graduate Studies, and make sure you have agreed ahead of time on what you will be required to do and how you will be graded. This is not necessary for those graduate courses that are cross-listed with undergraduate courses (315, 380, 381, 320, 325).
Yes. It is called the Yale Undergraduate Math Society, and arranges speakers, practices for the Putnam exam, and other activities. Check out their webpage, or email firstname.lastname@example.org for more information.
Not necessarily more calculus. There are a number of courses that either do not require or do not emphasize calculus, and offer a window into mathematical thinking.
- Math 228, From Euclid to Einstein: Geometry in the classical sense, and what it says about physics, philosophy and the development of mathematics.
- Math 190, Fractal Geometry: The study of "rough" sets of fractional dimension, and its relationship to nature and chaotic dynamics.
- Math 270, Set Theory: (120 is a prerequisite) The foundational underpinnings of mathematics, through the study of infinite sets.
- Math 244, Discrete Math: (115 recommended) the structure of finite sets, graphs, trees, and enumeration.
Try Math 101 or Math 108.
This depends on the situation. Typically we require at least half the courses toward the major to be taken at Yale, but the DUS must decide individually in each case.
Every year, one section of the senior seminar, 480, is dedicated to topics of interest to Econ/Math majors. The others are usually on a more pure-math subject, and the precise plan is worked out between the instructor and the participants in the beginning of the semester. Contact the instructor for details, or check the department web page.