Introduction to Higher Mathematics

Course Goals: This year-long class exposes students to six fundamental areas of mathematics. It is team taught by six members of the faculty. Fall topics include logic, set theory, combinatorics, and analysis. Spring topics include number theory, algebra, and geometry. Approximately 4 weeks is devoted to each topic. The class emphasizes rigorous proofs and concrete interesting examples. The class is not mandatory for prospective math concentrators, but it is strongly recommended.

Course Head (2017–2018): Jeffrey Hoffstein

Unit Instructors (2017–2018): Click for the webpage containing detailed information about individual units and instructors.

Unit #1 Logic and Set Theory Jill Pipher
Unit #2 Combinatorics Melody Chan
Unit #3 Analysis Brendan Hassett
Unit #4 Number Theory Jeffrey Hoffstein
Unit #5 Abstract Algebra Joe Silverman
Unit #6 Geometry Rich Schwartz

Grading: Mandatory S/NC

Textbook: Will be comprised of faculty course notes.

Exams per semester: One unit test at the end of each section, with the final exam being the unit test for the final unit of that semester.

Course meeting time (2017–2018, J hour): Tuesday–Thursday, 1:00–2:20pm

Learning Activities and Time Allocation: Learning activities include class attendance, weekly problem sets, and unit exam for each part of the course. The minimum time to complete these activities are (1) attending lectures, approximately 3 hours/week; (2) reading material in the book/course notes, approximately 2 hours/week; (3) working on the problem sets, approximately 8 hours/week.

Assessment: Course grades will be determined by the quality of problem sets submitted and by grades on the unit exams.

Expectations of Students: It is expected that students will attend all lectures and participate in class discussion in an appropriate manner. Assignments are due on the listed dates. All students are expected to abide by Brown's academic code, which may be  found here.

Math 750 Detailed Syllabus

Math 760 Detailed Syllabus