CMU Concepts 3 Week Prep

Categories: CMU, Mathematics
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About Course

This course provides a comprehensive yet concise guide on the first 3 weeks of content covered by CMU’s 21-128 course, Mathematical Concepts and Proofs, taught by Professor John Mackey. In this headstart program, Hagen Qian goes over Chapter 0: Fundamentals of Discrete Mathematics, Chapter 1: Propositional Logic and Basic Proofwriting Techniques, Chapter 2: Sets and Set Theory, and Chapter 3: Functions and Proving *jectivity and provides practice problems for students to apply their knowledge to.

What Will You Learn?

  • This course will cover the first 3 weeks of content of CMU's 21-128 course, Mathematical Concepts and Proofs. This includes 4 chapters worth of content, including:
  • Chapter 0: Fundamentals of Discrete Mathematics
  • Chapter 1: Propositional Logic and Basic Proofwriting Techniques
  • Chapter 2: Sets and Set Theory
  • Chapter 3: Functions and Proving *jectivity.

Course Content

Chapter 0: Fundamentals of Discrete Mathematics
This lecture covers topics covered in the pre-reading of the course, including quantifying variables, even and odd representation, and closure.

  • Chapter 0 Lecture
    18:16

Chapter 1: Propositional Logic and Proof Techniques
This lesson will cover propositional logics, constructing truth tables, and effective proof-writing techniques.

Chapter 2: Sets and Set Theory
This lecture covers set definitions, power sets, and double containment.

Chapter 3: Functions and Proving *jectivity
This lecture covers composite functions, images and preimages, and how to prove injectivity, surjectivity, and bijectivity.

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