# Mathematics

Mathematics has many aspects. It is the language and tool of the sciences, a key part of cultural development since ancient times, and a model of abstract reasoning. The course offerings and the major in Mathematics reflect these multiple facets. The Mathematics program provides a broad education in various areas of mathematics and is flexible enough to accommodate many interests. Mathematics majors have numerous options after graduation, including graduate study in mathematics or in various fields of application, government or corporate laboratory work, consulting, finance and banking, and teaching. Students considering a major in Mathematics are encouraged to consult with the director of undergraduate studies (DUS) during their freshman year.

A variety of resources is available to students who want additional help in any mathematics course:

- Each course instructor holds office hours for students multiple times a week.
- Undergraduate peer tutors associated with each calculus course provide help through regular office hours and private appointments.
- The Mathematics department offers coaching sessions for students in calculus courses.
- Drop-in tutoring with Math & Science Tutors is available in all residential colleges and at the Yale Center for Teaching and Learning in the Science & Quantitative Tutoring Program.

## Courses

A full description of all mathematics courses can be found in *Yale College Program of Study*. The department offers several courses that satisfy the QR distributional requirement and do not assume knowledge of mathematics beyond the basic high-school level. They include:

- MATH 107, Mathematics in the Real World
- MATH 108, Estimation and Error

The courses below include the ones most frequently taken by freshmen. Enrollment requires appropriate placement based on the online placement exam.

- MATH 112, Calculus of Functions of One Variable I, is the introductory course for students with a strong foundation in high school mathematics. It focuses primarily on differentiation and assumes no previous exposure to calculus.
- MATH 115, Calculus of Functions of One Variable II, builds on MATH 112 and focuses primarily on integration and infinite series. Knowledge of topics covered in MATH 112 is assumed.
- MATH 120, Calculus of Functions of Several Variables, combines the ideas and techniques of one-variable calculus with vector geometry and algebra to deal with geometrical situations in planes and in three-dimensional space. Knowledge of topics covered in MATH 112 and MATH 115 is assumed.

The courses below serve as options after MATH 112 for calculus students who have a specific focus. Students interested in the biological sciences should consider MATH 116, Mathematical Models in the Biosciences I: Calculus Techniques; those interested in economics should consider MATH 118, Introduction to Functions of Several Variables.

- MATH 116 is designed for bioscience and premedical students. It combines differential equations with geometrical modeling and applications in biology. Knowledge of topics covered in MATH 112 is assumed.
- MATH 118 is designed for students interested in economics and social sciences who do not intend to take additional mathematics courses. It covers basic ideas in linear algebra as well as differential calculus of several variables. Knowledge of topics covered in MATH 112 is assumed.

The higher-level courses below assume at least a year of calculus and are available to unusually well prepared freshmen.

- MATH 222, Linear Algebra with Applications, and MATH 225, Linear Algebra and Matrix Theory, deal with linear algebra, the common language for a wide variety of applications involving many variables. MATH 222 emphasizes computations and applications of linear algebra, while MATH 225 focuses on geometric and conceptual issues and the logical structure of the subject. Students normally take linear algebra after completing MATH 120, Calculus of Functions of Several Variables; however, students who are sufficiently prepared and motivated may take MATH 222 or MATH 225 concurrently with MATH 120.
- MATH 230, Vector Calculus and Linear Algebra I, and MATH 231, Vector Calculus and Linear Algebra II, is a demanding, two-term course sequence on calculus of many variables, designed for students with a firm grasp of one-variable calculus and a strong interest in mathematics. It emphasizes conceptual and logical structure and pays considerable attention to proofs and challenging problems. This course covers with greater rigor the material studied in MATH 120, MATH 225, and MATH 250, Vector Analysis, but assumes no prior knowledge of those topics.
- MATH 250, Vector Analysis, is a rigorous introduction to calculus of many variables, based on linear algebra. It focuses on proofs of calculus results and their generalizations to higher dimensions; knowledge of topics covered in MATH 120, and MATH 222 or MATH 225 is assumed. The sequence of MATH 120, MATH 222 or MATH 225, and MATH 250 serves as an alternative to MATH 230 and MATH 231 for the requirements of the Mathematics major.

Additional higher-level courses may be open to exceptionally well prepared freshmen. Interested students should seek advice from the director of undergraduate studies (DUS) or another knowledgeable faculty member.