Math 300 - Introduction to Mathematical Reasoning
Description
Math 300 is intended to be the first course a student takes involving abstract mathematical reasoning, including proof writing. For this reason, it is a core part of the mathematics major. It may also be counted towards a similar requirement for the Computer Science major—see the page on Math with Computer Science for more information.
Usually, one or two honors sections of 300 are offered each fall and spring. See the page on honors courses for more information.
Topics covered
Topics covered in Math 300 usually include:
- Basic mathematical language, including sets, quantifiers, related definitions
- Basic proof methods, including methods involving sets and induction
- Functions
- Injections, surjections, bijections
- Cardinality
- Relations
- Equivalence relations, including modular arithmetic
- Partial orders
Note that the exact list of topics may vary by instructor and semester. Additional topics may include basic real analysis (convergence of sequences).
Comments on prerequisites
For students who did not take 291, only one of 250 or 251 is needed to take Math 300. Having both courses completed before 300 may be helpful; some students think background from 250 is more relevant to 300 than 251.
Miscellaneous information
The official Math Department page about Math 300 contains a cautionary message. Most students who are serious about the possibility of studying further mathematics and understand what you are getting into by taking this course (abstract mathematics, not computational math like in calculus courses) should fare fine. If you are concerned about grade distributions of Math 300 students, recent distributions may be found here.
Resources
Textbook
Possible textbooks for the class include A Transition to Advanced Mathematics by Douglas Smith, Maurice Eggen, and Richard St Andre; and Book of Proof by Richard Hammack. Some iterations of the course do not closely follow a textbook.
Additional materials
A draft of a textbook based on 300H iterations taught by Michael Saks may be found online at https://sites.math.rutgers.edu/~saks/Mathematician’s%20Craft/.