KindiakMath

Discrete Math

Here are my write-ups on the theory of discrete math and some non-trivial exercises therein. Enjoy!

Theory

Logic

  1. The Logic of Logic
  2. Doing Logic the Lazy Way
  3. The Massive Impact of Applied Logic
  4. The Logic of Predicates
  5. Ground Zero Mathematics

Sets

  1. How to Nest Your Predicates
  2. Tying Up Loose Pairs
  3. Mathematical Relationships
  4. The Origin of Numbers
  5. Is 0 a Natural Number?

Number Theory

  1. Atomic Numbers
  2. What Makes Strong Induction Strong?
  3. Who Cares About Well-Ordering?
  4. A Classic Numbers Challenge

Functions

  1. What is a Negative Number?
  2. Creating the Integers
  3. A Partial Take on Partial Order
  4. Surjections as Sets
  5. Demystifying the Square Root

Cardinality

  1. The Preconditions of Infinity
  2. The Size of Finity
  3. Analysing Baby Infinity
  4. Counting the Fractions

Exercises

Logic

  1. Cheryl’s Birthday Problem

Sets

  1. Redefining Special Relations
  2. A Taste of Topology
  3. Measure-Theoretic Lingo

Number Theory

  1. A Fancy Multiples Problem
  2. Dividing Your Power
  3. Prime Factorisation
  4. Polynomial Long Division
  5. Theoretical Partial Fractions

Functions

  1. The Indicator Function
  2. Topological Continuity
  3. A Treatise on Measurability