Start Learning Mathematics

Overview

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Embark on a comprehensive 4.5-hour journey through fundamental mathematical concepts, starting with logic and progressing through sets, numbers, and complex numbers. Explore logical statements, set theory, natural numbers, integers, rational numbers, real numbers, and complex numbers. Dive into topics such as negation, conjunction, disjunction, tautology, predicates, functions, induction, and the completeness axiom. Learn about Greek letters used in mathematics and gain a solid foundation for further mathematical studies.

Syllabus

Start Learning Mathematics.
Start Learning Logic - Part 1 - Logical Statements, Negation and Conjunction.
Start Learning Logic - Part 2 - Disjunction, Tautology and Logical Equivalence.
Start Learning Logic - Part 3 - Conditional, Biconditional, Implication and Deduction Rules.
Start Learning Sets - Part 1 - Overview and Element Relation.
Start Learning Sets - Part 2 - Predicates, Equality and Subsets.
Start Learning Sets - Part 3 - Union, Intersection, Difference and Power set.
Start Learning Sets - Part 4 - Cartesian Product and Maps.
Start Learning Sets - Part 5 - Range, Image and Preimage.
Start Learning Sets - Part 6 - Injectivity, Surjectivity and Bijectivity.
Start Learning Sets - Part 7 - Composition of Maps.
Start Learning Numbers - Part 1 - Natural Numbers (in Set Theory).
Start Learning Numbers - Part 2 - Natural Numbers (Successor Map and Addition).
Start Learning Numbers - Part 3 - Natural Numbers (Induction and Associativity).
Start Learning Numbers - Part 4 - Natural Numbers (Ordering).
Start Learning Numbers - Part 5 - Natural Numbers (Multiplication).
Start Learning Numbers - Part 6 - Integers (Construction).
Start Learning Numbers - Part 7 - Integers (Addition and Inverses).
Start Learning Numbers - Part 8 - Integers (Multiplication).
Start Learning Numbers - Part 9 - Rational Numbers (Construction).
Start Learning Numbers - Part 10 - Rational Numbers (Addition and Multiplication).
Start Learning Numbers - Part 11 - Rational Numbers (Ordering).
Start Learning Reals - Part 1 - Cauchy Sequences.
Start Learning Reals - Part 2 - Completeness Axiom.
Start Learning Reals - Part 3 - Working With Axioms.
Start Learning Reals - Part 4 - Construction.
Start Learning Complex Numbers - Part 1 - Introduction.
Start Learning Complex Numbers - Part 2 - Definition.
Start Learning Complex Numbers - Part 3 - Absolute Value, Conjugate, Argument.
Greek Letters in Mathematics.