Book of Proof by Richard Hammack (Free online).
While Grant Sanderson (3B1B) focuses on calculus and linear algebra, his video "How to lie using visual proofs" is directly applicable to 18.090’s section on invalid arguments and fallacies.
The course moves away from "plug-and-chug" computation and focuses heavily on constructing logical arguments, creating proofs, and understanding the foundational principles of mathematics.
that communicates mathematical truths unambiguously. Identify flaws in seemingly correct mathematical arguments. The Anatomy of Mathematical Logic Book of Proof by Richard Hammack (Free online)
Assuming the opposite of what you want to prove and showing it leads to a logical impossibility.
: You will develop the ability to write and present mathematical proofs effectively. MIT Mathematics Standard Topics Covered
), and truth tables. Understanding the exact linguistic definition of conditionals ( ) prevents systemic errors in later proof construction. 2. Set Theory and Functions that communicates mathematical truths unambiguously
Mastering the Transition to Higher Math: A Deep Dive into MIT's 18.090
If you are currently working through these concepts, let me know how I can help you master them. I can provide , break down a specific proof technique in deeper detail, or look over a proof draft you are working on to suggest improvements. Share public link
Writing a high-quality mathematical proof requires more than just correct logic. It requires clarity and style. MIT graders look for specific elements that elevate a proof from mediocre to exceptional. : You will develop the ability to write
: Truth values, predicates, quantifiers, and logical notation (
Applying proofs to actual mathematical landscapes. Core Proof Techniques Mastered in 18.090
Example: Proving that the sum of two even integers is always even. 2. Proof by Contradiction (Reductio ad Absurdum)
A direct logical progression from axioms to the conclusion. Contrapositive: Proving by showing