Course Learning Outcomes
- Department: Mathematics
- Course number: 30800
- Course title: Bridge to Advanced Mathematics
- Term offered: Spring 2024
- Pre/co-requisites: A grade of C or higher in MATH 21300 or placement by the department
- Hours and credits: 3 hours and 3 credits
- Date effective: May 30, 2024
- Course coordinator: Hooper
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.
Typical textbooks used
- Gary Chartrand, Albert D. Polimeni, and Ping Zhang, Mathematical Proofs: A Transition to Advanced Mathematics, 4th edition, Pearson, 2018
- Kenneth A. Ross, Elementary Analysis: The Theory of Calculus, 2nd edition, Springer, 2013.
The Ross textbook is available for free download from the CCNY library through SpringerLink. Try the link above.
Course learning outcomes:
| After taking this course, the students should be able to: | Contributes to Departmental learning outcome(s): |
|---|---|
| 1) Demonstrate an ability to understand and manipulate mathematical statements involving quantifiers and logical connectives. Examples of manipulations include finding the negation, converse, and contrapositive of a quantified implication | a, g |
| 2) Write clear and rigorous proofs (or disproofs) of mathematical statements utilizing basic proof techniques including direct proof, proof by contrapositive, proof by contradiction, proof by cases, mathematical induction, and by providing an example (or counterexample). | e1, e2, f, g |
| 3) Demonstrate knowledge of fundamental concepts of mathematics including those relating to logic, sets, functions, relations, cardinality, integers, rationals and reals. Precisely state fundamental definitions, axioms and theorems and utilize them to prove related results. | a, e1, e2, f, g |
Course assessment tools
Left up to instructor. (Instructor: Please adjust and insert percentages.) Typical assessment tools:
- Attendance
- Homework and/or Quizzes
- Midterms
- Final Exam
Departmental learning outcomes:
The mathematics department, in its varied courses, aims to teach students to:
- a) perform numeric and symbolic computations
- b) construct and apply symbolic and graphical representations of functions
- c) model real-life problems mathematically
- d) use technology appropriately to analyze mathematical problems
- e) state (e1) and apply (e2) mathematical definitions and theorems
- f) prove fundamental theorems
- g) construct and present (generally in writing, but, occasionally, orally) a rigorous mathematical argument.