Math for Non-Geeks

Title image of the German version by Olivier Vidal

IMPORTANT NOTE - WORK IN PROGRESS - DO NOT DELETE

This is NOT A RANDOM EXPERIMENTATION with wikibooks, but I am trying to transfer the following three existing books from de.wikibooks.org to en.wikibooks.org, which I translated over the past 4 years from German into English:

• Linear Algebra 1
• Measure Theory
• Real Analysis 1

PLEASE DO NOT DELETE!!!

I am currently very busy with work and could not get any information about how the original code on de.wikibooks.org was created or stored. So it may take some time.

If you know wikibooks better than me, you are very welcome to help me transfer the three above-mentioned books and their first page here, including the "#invoke"-environments.

Table of Contents

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.

Legend

Symbol	Meaning
red link	Link to a chapter that does not yet exist and has yet to be written.
blue link	Chapter has already been created and contains content.
	Progress 0% – Chapter has little or no content. The chapter must be rewritten or supplemented and revised.
	Progress 25% – Chapter is currently under development, but still needs to be significantly expanded.
	Progress 50% – Essential content is available, but important content still needs to be added (there are often ToDo notes on the page that still need to be added).
	Progress 75% – Chapter is finished in terms of content, but still needs to be revised (correct spelling mistakes, change wording so that it is easier to understand or sounds better. Remove redundant expressions).
	Progress 100% – The chapter is complete and has been proofread at least once. But you can also proofread again. In other words: correct spelling mistakes and improve the wording. These chapters (like all others) can also be supplemented content-wise.

Real Analysis

Help

• Translating chapters
• Guidelines for translation

Introduction

• What is analysis?
• Why study analysis?
• Propositional logic
• Mathematical induction
• Real numbers

Complex numbers

• Introduction and motivation
• Definition of complex numbers
• Absolute value and conjugation
• Polar representation
• Drawing complex-valued functions
• Exercises: Complex numbers

Suprema and infima

• Suprema and infima
• The infinite case
• How to prove existence of a supremum or infimum
• Properties of suprema and infima

Sequences

• Sequences
• Explicit and recursive description
• Examples and properties of sequences
• Exercises: Sequences

Convergence and divergence

• Limit: Convergence and divergence
• How to prove convergence and divergence
• Examples for limits
• Unbounded sequences diverge
• Limit theorems
• The squeeze theorem
• Monotony criterion
• How to prove convergence for recursive sequences
• Exercises: Convergence and divergence

Subsequences, Accumulation points and Cauchy sequences

• Subsequences
• Accumulation points of sequences
• Accumulation points of sets
• The Bolzano-Weierstrass theorem
• Divergence to infinity
• Divergence to infinity: Rules
• Limit superior and limit inferior
• Cauchy sequences
• Exercises: Subsequences, Accumulation points, and Cauchy sequences

Series

• 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: Series

Convergence criteria for series

• 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: Convergence criteria for series

Exponential and Logarithm functions

• Derivation and definition of the exponential series
• Properties of the exponential series
• Logarithmic functions
• Real exponents
• Exponential and logarithm functions for complex numbers
• Exercises: Exponential and logarithm functions

Trigonometric and Hyperbolic functions

• Sine and cosine

Continuity

• 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: Continuity

Differential Calculus

• Derivatives
• Computing derivatives
• Computing derivatives - special
• Derivative - inverse function
• Examples for derivatives
• Derivatives of higher order
• Rolle's theorem
• Mean value theorem
• Constant functions
• Monotone functions
• Derivative and local extrema
• L'Hôpital's rule
• Overview: Continuity and differentiability
• Exercises: Derivatives 1
• Exercises: Derivatives 2
• Exercises: Derivatives 3
• Exercises: Derivatives 4

Linear algebra

Vector spaces

• Introduction to 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

• Linear combinations
• Span
• Generators
• Linear independence
• Basis
• Steinitz's theorem
• Dimension

Linear maps

• Linear maps
• 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: Linear Maps

Matrices

• 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: Matrices

Measure theory

Introduction, basic definitions

• Overview: Objects in measure theory
• Volumes on rings
• Continuity of volumes on rings
• Pre-measures and measures

Constructing measures

• Constructing measures: Overview
• Generated sigma-algebras
• Existence of a measure continuation
• Uniqueness of a continuation

Here, some links should appear to the books linked in the Sitemap

I am currently translating all Lua modules to make this work.