Math for Non-Geeks
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Books
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Important note
[edit | edit source]This book is a translated version of the book project “Mathe für Nicht-Freaks” on the German version of Wikibooks. Templates and modules do not yet work completely and are in the process of being adjusted.
Table of Contents
[edit | edit source]This page lists all chapters of the project “Math for Non-Geeks”. This page serves as an overview and the complete navigation and the tables of contents of the individual books are generated from it.
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Help
[edit | edit source]Introduction
[edit | edit source]Complex numbers
[edit | edit source]- Introduction and motivation
- Definition of complex numbers
- Absolute value and conjugation
- Polar representation
- Drawing complex-valued functions
- Exercises
Suprema and infima
[edit | edit source]- Supremum and infimum
- The infinite case
- How to prove existence of a supremum or infimum
- Properties of supremum and infimum
Sequences
[edit | edit source]Convergence and divergence
[edit | edit source]- Limit: Convergence and divergence
- How to prove convergence and divergence
- Examples for limits
- Unbounded sequences diverge
- Limit theorems
- The squeeze theorem
- Monotonicity criterion
- How to prove convergence for recursive sequences
- Exercises
Subsequences, Accumulation points and Cauchy sequences
[edit | edit source]- Subsequences
- Accumulation points of sequences
- Accumulation points of sets
- The Bolzano-Weierstrass theorem
- Divergence to infinity
- Divergence to infinity: Rules
- Superior and inferior limit
- Cauchy sequences
- Exercises
Series
[edit | edit source]- Series
- Computation rules for series
- Telescoping sums and series
- Geometric series
- Harmonic series
- Exponential series
- Absolute convergence of a series
- Rearrangement theorem for series
- Exercises
Convergence criteria for series
[edit | edit source]- Overview: Convergence criteria
- Cauchy criterion
- Term test
- Bounded series and convergence
- Direct comparison test
- Root test
- Ratio test
- Alternating series test
- Cauchy condensation test
- Application of convergence criteria
- Exercises
Exponential and Logarithm functions
[edit | edit source]- Derivation and definition of the exponential series
- Properties of the exponential series
- Logarithmic function
- Real exponents
- Exp and log functions for complex numbers
- Exercises
Trigonometric and Hyperbolic functions
[edit | edit source]Continuity
[edit | edit source]- Continuity of functions
- Epsilon-delta definition of continuity
- Sequential definition of continuity
- Limit of functions
- Proving continuity
- Proving discontinuity
- Composition of continuous functions
- Extreme value theorem
- Intermediate value theorem
- Continuity of the inverse function
- Uniform continuity
- Lipschitz continuity
- Exercises
Differential Calculus
[edit | edit source]- Derivatives
- Computing derivatives
- Computing derivatives - special
- Derivative - inverse function
- Examples for derivatives
- Derivatives of higher order
- Rolle's theorem
- Mean value theorem
- Constant functions
- Monotonic functions
- Derivative and local extrema
- L'Hôspital's rule
- Overview: continuity and differentiability
- Exercises 1
- Exercises 2
- Exercises 3
- Exercises 4
Vector spaces
[edit | edit source]- Introduction: Vector space
- Vector space
- Vector space: properties
- Proofs for vector spaces
- Field as a vector space
- Coordinate spaces
- Sequence spaces
- Function spaces
- Subspace
- Union and intersection of vector spaces
- Sum of subspaces
- Inner direct sum
- Complements of vector spaces
- Cosets of a subspace
- Quotient space
Linear combinations, generators and bases
[edit | edit source]Linear maps
[edit | edit source]- Linear map
- Properties of linear maps
- Linear continuation
- Proofs for linear maps
- Monomorphisms
- Epimorphisms
- Isomorphisms
- Endomorphism and Automorphism
- Image of a linear map
- Kernel of a linear map
- Vector space of a linear map
- Dual space
- Exercises
Matrices
[edit | edit source]- Introduction: Matrices
- Matrix of a linear map
- Definition of a matrix
- Linear systems and matrices
- Vector space structure on matrices
- Matrix multiplication
- Basis change via matrices
- Exercises
Introduction, basic definitions
[edit | edit source]- Overview: Objects in Measure Theory
- Volumes on rings
- Continuity of volumes on rings
- Pre-measures and measures