Math for Non-Geeks
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:
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.
| 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
Complex numbers
- Introduction and motivation
- Definition of complex numbers
- Absolute value and conjugation
- Polar representation
- Drawing complex-valued functions
- Exercises
Suprema and infima
- Supremum and infimum
- The infinite case
- How to prove existence of a supremum or infimum
- Properties of supremum and infimum
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
- Monotonicity criterion
- How to prove convergence for recursive sequences
- Exercises
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
- Superior and inferior limit
- Cauchy sequences
- Exercises
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
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
Exponential and Logarithm functions
- 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
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
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
- Monotonic functions
- Derivative and local extrema
- L'Hôspital's rule
- Overview: continuity and differentiability
- Exercises 1
- Exercises 2
- Exercises 3
- Exercises 4
Linear algebra
Vector spaces
- 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
Linear maps
- 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
- 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
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.
Script error: No such module "Mathe für Nicht-Freaks/Seite".