ABSTRACT

Bridging the gap between procedural mathematics that emphasizes calculations and conceptual mathematics that focuses on ideas, Mathematics: A Minimal Introduction presents an undergraduate-level introduction to pure mathematics and basic concepts of logic. The author builds logic and mathematics from scratch using essentially no background except n

part |2 pages

Part 1. Pre-mathematical logic

chapter 1|10 pages

Languages

chapter 2|6 pages

Metalanguage

chapter 3|6 pages

Syntax

chapter 4|4 pages

Semantics

chapter 5|6 pages

Tautologies

chapter 6|2 pages

Witnesses

chapter 7|6 pages

Theories

chapter 8|6 pages

Proofs

chapter 9|4 pages

Argot

chapter 10|4 pages

Strategies

chapter 11|8 pages

Examples

part |2 pages

Part 2. Mathematics

chapter 12|4 pages

ZFC

chapter 13|6 pages

Sets

chapter 14|4 pages

Maps

chapter 15|6 pages

Relations

chapter 16|6 pages

Operations

chapter 17|4 pages

Integers

chapter 18|4 pages

Induction

chapter 19|2 pages

Rationals

chapter 20|2 pages

Combinatorics

chapter 21|2 pages

Sequences

chapter 22|2 pages

Reals

chapter 23|4 pages

Topology

chapter 24|2 pages

Imaginaries

chapter 25|4 pages

Residues

chapter 26|2 pages

p-adics

chapter 27|4 pages

Groups

chapter 28|2 pages

Orders

chapter 29|2 pages

Vectors

chapter 30|4 pages

Matrices

chapter 31|4 pages

Determinants

chapter 32|4 pages

Polynomials

chapter 33|4 pages

Congruences

chapter 34|4 pages

Lines

chapter 35|2 pages

Conics

chapter 36|4 pages

Cubics

chapter 37|4 pages

Limits

chapter 38|4 pages

Series

chapter 39|2 pages

Trigonometry

chapter 40|4 pages

Integrality

chapter 41|4 pages

Reciprocity

chapter 42|4 pages

Calculus

chapter 43|4 pages

Metamodels

chapter 44|6 pages

Categories

chapter 45|4 pages

Functors

chapter 46|4 pages

Objectives

part |2 pages

Part 3. Mathematical logic

chapter 47|4 pages

Models

chapter 48|4 pages

Incompleteness