Bridge to Advanced Mathematics
Math 308 · Fall 2026 · CCNY
Instructor: Keino Brown, Ph.D.
Email: [email protected]
Office hours: Tuesdays & Thursdays 12:00–1:00 PM — book a slot
Meeting: Section EF Days/Time MoWe 2:00PM - 3:40PM Room NAC 5/102
Course Catalog Description
This course explores the logical and foundational structures of mathematics, with an emphasis on understanding and writing proofs. Topics include set theory, logic, mathematical induction, relations and orders, functions, Cantor’s theory of countability, and development of the real number system. For more information and course resources, see here.
Prerequisite
A grade of C or higher in MATH 20300 or MATH 21300, or placement by the Department.
Texts
Mathematical Proofs: A Transition to Advanced Mathematics (4th ed.) by Chartrand, Polimeni, and Zhang (ISBN: 978-0134746753).
Supplementary: Elementary Analysis: The Theory of Calculus (2nd ed.) by Kenneth A. Ross (Chapter 1 is freely available via Springer; follow the link above for a copy.)
Learning Outcomes
See the Course Learning Outcomes.
Assessment
There are no make-ups, no curves, and no extra credit.
| When | What | Weight |
|---|---|---|
| Sept 30, Oct 28, Nov 23 | Exam 1, Exam 2, Exam 3 | 60 points (top 2 of 3) |
| TBA, Final Exam period (Dec 15–21) | Final Exam | 40 points |
Weighted score
(average of top 2 exam scores) × 0.60 + (final exam score) × 0.40
Letter Grades
Based on your weighted score:
| A+ 97–100 | B+ 87–89 | C+ 77–79 | F <60 |
| A 95–96 | B 84–86 | C 70–76 | |
| A- 90–94 | B- 80–83 | D 60–69 |
Homework
Homework problems are assigned to prepare you for the in-class exams; your grade is based on the exams.
Attendance/Lateness
Regular and consistent attendance is required. No more than three (3) absences will be excused. Whenever you are going to be absent, email me before class starts that day to request an excused absence. Leaving before class ends counts as an absence; arriving after attendance is taken counts as late, and three (3) latenesses count as one (1) unexcused absence. More than three (3) unexcused absences reduces your letter grade by one. You are responsible for any work missed while absent.
Electronics Policy
Calculators and electronic devices of any kind are not permitted during exams.
Academic Integrity
DO NOT CHEAT. Cheating results in an immediate, non-negotiable F. See the university’s policy on academic integrity here.
Students with Disabilities
If you receive accommodations for test taking, please contact the AccessAbility Center in NAC 1/218, 212-650-5913, or [email protected] to schedule your exams.
Exam Schedule
| When | What | Topics |
|---|---|---|
| Sept 30 | Exam 1 | Writing proofs, logic, and sets (Ch 1–3) |
| Oct 28 | Exam 2 | Direct and conditional proofs, existence & counterexamples, induction (Ch 4–7) |
| Nov 23 | Exam 3 | Relations, functions, cardinality (Ch 8–10) |
| Dec 15–21 | Final | Comprehensive (incl. the integers, Ch 11 and Completeness Axiom, Chapter 1, Ross) |
The lowest of the first three exam scores is dropped; an absence on one of the first three exams counts as the dropped score. There are no make-ups, no curves, and no extra credit. Because the final is 40% of your grade, taking the final is necessary (but not sufficient) to pass.
Tentative Course Schedule
(M/W; subject to change):
| Week of | Monday | Wednesday |
|---|---|---|
| Aug 31 | Intro; Sets §1.1–1.3 | Sets §1.4–1.6 |
| Sep 7 | Labor Day — no class | Logic: statements, implications |
| Sep 14 | Logic: quantifiers | Direct proof & contrapositive |
| Sep 21 | No class | Proof by cases; “if and only if” |
| Sep 28 | Review | Exam 1 (Ch 1–3) |
| Oct 5 | Ch 4: divisibility, congruence | Ch 4: real numbers, sets |
| Oct 12 | Closed — Tue 10/13 (Mon sched.): Ch 5 | Ch 5: counterexamples, uniqueness |
| Oct 19 | Ch 6: induction | Ch 6: strong induction; Ch 7 review |
| Oct 26 | Review | Exam 2 (Ch 4–7) |
| Nov 2 | Ch 8; Ch 9: relations | Ch 9: equivalence relations |
| Nov 9 | Ch 9: congruence mod n | Ch 10: injective/surjective/bijective |
| Nov 16 | Ch 10: composition, inverses | Review |
| Nov 23 | Exam 3 (Ch 8–10) | No class — Thanksgiving |
| Nov 30 | Ch 11: cardinality | Ch 11: Cantor, Schröder–Bernstein |
| Dec 7 | Ross Ch 1: ℕ,ℚ,ℝ | Ross Ch 1: Completeness Axiom |
| Dec 14 | Comprehensive review | Final Exams Dec 15–21 |
No classes on (college closures, Fall 2026)
Mon 9/7 (Labor Day) — College closed
9/11–9/13 — No classes scheduled
Mon 9/21 — No classes scheduled
Mon 10/12 — College closed (Tue 10/13 follows a Monday schedule)
Wed 11/25 — No classes scheduled
11/26–11/27 (Thanksgiving) — College closed
Sat 11/28 — No classes scheduled