Course Description

This is a course in real analysis. Topics include the real number system and functions of a single real variable, definitions of, and theorems involving limits, sequences, series, convergence, continuity, differentiation, and integration. Together these topics provide a formal study of the foundations of single-variable calculus. Although most of these topics are covered in calculus, the treatment here focuses on theory rather than on computation and applications. For example, a calculus course teaches methods for differentiating and integrating functions, shows how these operations can be understood in terms of rates of growth of functions and areas under curves, and demonstrates the power of calculus through real-world applications. In contrast, this course operates in an abstract setting and aims to develop a robust understanding of definitions and theorems, including their proofs. With this emphasis, students in this course will learn how to read and write mathematical proofs.

Honors math majors and students who intend to do graduate work in math should take 171.

Per University policy, your decision to take the course implies that you agree to these requirements and to the grading policies spelled out here; so be sure to read everything on these pages.

Schedule:

Text:

One of the goals of the class is to teach you to read mathematical text. That is why we'll try to stick to the textbook: We recommend that you print out the relevant pages, since we find that students more deeply engage with printed rather than electronic materials.

Course website:

Most of the materials will be posted on this website: math115.stanford.edu Some course announcements will be posted through Canvas.

Grades:    

Resources:

You are encouraged to attend the office hours provided by the instructor and course assistant.
Another resource which may be of use is Counseling and Psychological Services. See vaden.stanford.edu/caps-and-wellness.
For background for logic and proof-writing see Michael Hutchings' 'Introduction to mathematical arguments'. You are not required to read this, but if you feel uneasy about e.g. the connectives or quantifiers above you can look them up there.

Access and Accommodations

Special situations adaptations

As standard practice, lectures are conducted in person. As such, Zoom links will not be provided. Additionally, in-person lectures will not be recorded.

Students who miss class due to illness (including COVID-19) should make arrangements to obtain lecture notes from other students in the class. As standard practice, there are no make-up exams or remote exams. If you will miss an exam due to illness, please reach out to your instructor for more information.


Autumn 2025
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