Math 300: Introduction to Mathematical Reasoning
Rutgers University
Instructor: Tom Benhamou
My Office: Hill 205
Office hours: Wed 11:00 am to 12:00 pm
E-Mail tom.benhamou (at) rutgers (dot) edu
Wed 12:10pm to 1:30pm and Fri 2:00pm to 3:20pm at TIL-127 (LIV)
Textbook: Douglas Smith, Maurice Eggen, Richard St. Andre, A Transition to Advanced Mathematics 8th Edition.
Description
The propose of this course is to grant the students with the necessary tools to access advance mathematics. The main difficulty you will encounter during the shift to advance mathematics is the high standard of formality used by mathematicians. We will put an emphasize on this matter, especially on writing proofs. The second part of the course is devoted to the development of
Set Theory and the mathematical universe which is the place where most regular mathematics (such as Calculus, Linear Algebra, Probability, Combinatorics etc.) occurs.
Final Grade
The final grade will be based on the results of the examinations and the solutions of the homework problems. Here are the weights of the different components of the course:
- Homework 20%
- Workshop and Class participation 10%
- Midterm I 15%- 10/18 during class time
- Midterm II 15%- 11/27 during class time
- Final exam 40%
Workshop-2024
We will have an hour a week of a workshop where we practice proof writing in class.
Workshop-2023
Home Work
HW will be assigned weakly on Friday and are due the following Friday. Please submit your solutions on the Canvas platform in a clear, readable, properly scanned, unrotated single pdf file.
Home Work Solutions:
Class Notes:
Chapter 1: Introduction to Mathematical Logic
Chapter 2: Formal Proofs
Chapter 3: Basic Set Theory and Induction
Chapter 4: Functions
Chapter 5: Equinumerability
Chapter 6: Equivalence Relations
Exams:
Midterm 2024
Midterm 2024-sols
Midterm 2023 Solutions
Midterm example 1
Midterm example 1-Solutions
Midterm example 2
Midterm example 2-Solutions
Midterm 2-Perparation
Midterm 2-Preparation Solutions
Midterm 2 2023
Finals-Exmaple
Finals-Preparation problems
Finals-Preparation problems Solutions
Other material:
Syllabus
Writing a Mathematical Proof
Logic Identities
Set Operations Identities