What Is Mathematics Courant And Robbins Matt Parker Pdf Github

Math - Where math is used

Algorithms

How Reddit ranking algorithms work
Recounting the Rationals - a process for listing all rational numbers

Applications of Math to Real-World Problems

Real-world applications of mathematics, by arxiv subject area?

Art

Rafael Araujo on mathematical illustrations of nature

Astronomy

The Cosmic Distance Ladder - History of Measuring Distances to Heavenly Bodies - Terence Tao discusses how we have determined the distance to the moon, sun, planets, and so on, describing the mathematics and technology at each 'rung' of the ladder.
Why Do Planets Have Elliptical Orbits - 3Blue1Brown explains using math why orbits are elliptical. A paper explaining the same argument is here.

Biology

Ants Estimate Area Using Buffon's Needle
- Accuracy of Buffon's Needle
In defence of doing sums in genetics - "There has been a long history of the use of mathematics in genetics, ranging from the use of statistics to analyse genetic data to genetic models of evolutionary processes. Contemporary research into the genomic basis of disease and complex traits exemplifies the importance of statistical methods in genetics. Some examples of the development and application of population genetic models are described, which are intended to highlight the utility of such models for understanding variation and evolution in natural populations. The effects of selection on variability at sites linked to the targets of selection illustrate how fruitful interactions between theory and data can be."
Statistical mechanics for natural flocks of birds - modelling flock behaviour From the article: "Flocking is a typical example of emergent collective behavior, where interactions between individuals produce collective patterns on the large scale. Here we show how a quantitative microscopic theory for directional ordering in a flock can be derived directly from field data. We construct the minimally structured (maximum entropy) model consistent with experimental correlations in large flocks of starlings."
Math Sheds Light on How Living Cells 'Think'
- News article
- Journal source
The Chemical Basis of Morphogenesis - A.M.Turing (1952)
Seashells: The plainness and beauty of their mathematical description - Jorge Picado

Biomimicry

Short video explaining biomimicry
Sea Urchin Spines Inspire Elastic Concrete
Slime Mold Grows Network Just Like Tokyo Rail System
Water filter inspired by Alan Turing passes first test: Membrane's structure predicted in mathematician's lone biology paper
Soldier Crab Logic Gate Abstract: Soldier crabs Mictyris guinotae exhibit pronounced swarming behaviour. The swarms of the crabs tolerant of perturbations. In computer models and laboratory experiments we demonstrate that swarms of soldier crabs can implement logical gates when placed in a geometrically constrained environment.

Business

Probability Models for Customer-BaseAnalysis Paraphrased from the pdf: "Faced with a customer transaction database, we may wish to determine: which customers are most likely to be active in the future; the level of transactions we could expect in future periods from those on the customer list, both individually and collectively; and–individual customer lifetime value."

Coffee

Systematically Improving Espresso: Insights from Mathematical Modeling and Experiment

Complex Numbers

Quaternions

Quaternions are used for 'calculations involving three-dimensional rotations', such as in aeronautics and robotics.

Computing

A Mathematical Theory of Communication - C.E.Shannon
The Byzantine Generals Problem
The Halting Problem
Computational capacity of the universe
The Maniac 1"The MANIAC I (Mathematical Analyzer Numerical Integrator and Automatic Computer Model I) was an early computer built under the direction of Nicholas Metropolis at the Los Alamos Scientific Laboratory."
The Maniac 1 - computer manual

Cryptography

Short discussion about the history of cryptography
A Masked White-box Cryptographic Implementation for Protecting against Differential Computation Analysis - Seungkwang Lee (2017)
Repository of various public white-box cryptographic implementations and their practical attacks

Digital Signal Processing - Audio, Visual, and Other

Audio-Visual Speech Separation - Separating Audio Tracks From Video "People are remarkably good at focusing their attention on a particular person in a noisy environment, mentally "muting" all other voices and sounds. Known as the cocktail party effect, this capability comes natural to us humans. However, automatic speech separation — separating an audio signal into its individual speech sources — while a well-studied problem, remains a significant challenge for computers." The paper can be found here.
Digital Signal Processing To quote the author of the guide in the link above: "Digital Signal Processing is one of the most powerful technologies that will shape science and engineering in the twenty-first century. Revolutionary changes have already been made in a broad range of fields: communications, medical imaging, radar & sonar, high fidelity music reproduction, and oil prospecting, to name just a few. Each of these areas has developed a deep DSP technology, with its own algorithms, mathematics, and specialized techniques."

Discrimination

Jewish Problems From the abstract: "This is a special collection of problems that were given to select applicants during oral entrance exams to the math department of Moscow State University. These problems were designed to prevent Jews and other undesirables from getting a passing grade. Among problems that were used by the department to blackball unwanted candidate students, these problems are distinguished by having a simple solution that is difficult to find. Using problems with a simple solution protected the administration from extra complaints and appeals. This collection therefore has mathematical as well as historical value." The author's website is here: http://www.tanyakhovanova.com/Coffins/coffinsmain.html

Elections

Arrow's Theorem (or: How I Learned to Stop Worrying and Love Dictatorships)

Gerrymandering:

You can't tell a gerrymandered district by its shape
An impossibility theorem for gerrymandering

Elevator Logistics

Elevator Saga The elevator programming game

Games

Gamedev Tutorial: Dot Product, Rulers, And Bouncing Balls
The Mathematical Beauty of the Game SET
Demo-Man - Interactive gamedev tutorialsTrigonometry and vector mathematics in basic videogame development.
Math for Game Programmers: Interaction With 3D GeometryVector maths for videogames.
Pysically Based Rendering - From Theory to Implementation
Ray Tracing Essentials Part 1: Basics of Ray Tracing
Rubik's Cube - God's Number is 20
Rubik's Cube - UWaterloo pdf
The Mathematics of the Rubik's CubeIntroduction to Group Theory and Permutation Puzzles
Group Theory and the Rubik's Cube - Janet Chen
Three Statistical Tests Every Game Developer Should Know
Unreal Engine Optimized Post-Effects

Infinity

Infinity and the Mind

Knots

Knots - Mathematicians are devising new techniques to better predict how to tie strong knots that are useful in climbing and sailing

Literature

Cadaeic Cadenza - Writing poetry where each word-length denotes successive digits of pi

Maps

The topologist's world map

Movies - Special Effects

3D Modelling Techniques Worthy of an Oscar - "Some of his early research focused on how to realistically depict "gaseous natural phenomena" like curling wisps of smoke, mist over a field or car exhaust while they react to a "turbulent field" like wind. His graphics, like a steaming cup of coffee, look simple in hindsight, but were anything but in the early 1990s.... His work on fast fluid flow computation in particular introduced techniques that were a breakthrough in visual fluid simulation and has deeply influenced dozens of researchers over the past 20 years."
Pixar - Online library - Has many technical memos on CGI work.

Networks - Social and Political Connections

Networks, Crowds, and Markets: Reasoning about a Highly Connected World (David Easley and Jon Kleinberg, CUP, 2010. - The author writes: "Here we describe a rich part of social network theory that involves taking a network and annotating its links (i.e., its edges) with positive and negative signs. Positive links represent friendship while negative links represent antagonism, and an important problem in the study of social networks is to understand the tension between these two forces.." The complete preprint is available on-line at http://www.cs.cornell.edu/home/kleinber/networks-book/.
The Polarization of Society: Even Scientists Become Tribal - The authors, Cailin O'Connor and James Owen Weatherall, argue that polarization is the natural outcome when groups of people disagree. In fact, they document a major example of polarization within the scientific community itself.
The Evolution of Trust

Philosophy

The 'Square of Opposition', a collection of logical relationships traditionally embodied in a square diagram.

Programming

Is the room open? Programming problem

Physics

A Collector of Math and Physics Surprises - Tadashi Tokieda
Gears

Proofs

Book of Proof - Hammack
How to Read and Understand Proofs

Science

What to do when you don't trust your data anymore

Sound and Sine Waves

Encoding data in dubstep drops

Statistics, data management, probability

Game Track - Covering the gaming market
German Tank Problem
Heart doctors 'held back stent death data'
Mathematics of Machine Translation - Algorithms for translating languages
Multi-Armed Bandit(MAB) – A/B Testing Sans Regret
Private traits and attributes are predictable from Facebook 'likes'
Variance - Advancing the Science of Risk (Journal) - "Variance is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science."

Traffic

Vehicle Routing Problem
Boarding Airplanes - What is the fastest way?
The case for almost never turning left while driving - UPS
Why UPS drivers don't turn left and you probably shouldn't either

Trigonometry

Apollo 11 implementation of trigonometric functions "This code was submitted by Margaret H. Hamilton (Programming Leader Apollo Guidance and Navigation) in March 1969 and was used to evaluate trigonometric functions essential for navigation on both the Command Module and Lunar Lander that ﬁrst landed humans on the Moon."

Vectors

Game Design - Programming Track Visuals in SNES game F-Zero

Where not using math, or using math poorly, can cause problems

Spain builds submarine 70 tons too heavy after putting a decimal in the wrong place
Nov. 10, 1999: Metric Math Mistake Muffed Mars Meteorology Mission
Upside-Down Sensors Toppled Russian Rocket
What Happens When Maths Goes Wrong? with Matt Parker - "You can find any pattern you want to any level of precision you want as long as you're prepared to ignore enough data."
Beyond Reasonable Doubt - The Story of Sally Clark (Bayes' Theorem used in court case)
Honda Needs a Tune-Up - "A musical road that Honda built in Lancaster, CA.. A team of engineers carved some grooves into a highway that were carefully spaced to play the William Tell Overture as you drive over them at a constant speed."

Recreational Mathematics

Puzzles

Alex Bellos' Monday Puzzle - The Guardian
Project Euler

Math-related Games

A Slower Speed of Light
Euclidea
Factorio
HyperRogue
Jelly no Puzzle
Kerbal Space Program
Manufactoria
Miegakure
Minecraft
Portal
Spacechem
Talos Principle
Natural Number Game
other suggestions-redditthread

Making Drawings

Escher
Dragon Curve
Golden Spiral
Appolonian Gasket, Serpinski Triangle, etc
Barnsley Fern

Math Resources

Biographies

An Evening with Leonhard Euler
Fermat
- Andrew Wiles' historical Fermat's Last Theorem talk at the 1998 ICM
- Fermat's Last Theorem - The Theorem and Its Proof: An Exploration of Issues and Ideas [1993]
J. von Neumann

Books

http://linear.ups.edu/curriculum.html

Home page for the book, Bayesian Data Analysis, by Gelman, Carlin, Stern, Dunson, Vehtari, and Rubin.
Open Logic Project - "open-source, collaborative textbook of logic and formal methods, starting at an intermediate level, aimed at a non-mathematical audience."
Living Proof: Stories of Resilience Along the Mathematical Journey

Courses

MIT Open Courseware
OpenStax - Free textbooks for Algebra, Calculus, Statistics for highschool and undergraduate studies.
Introduction to probability, statistics, and random processes
Statistics 110: Probability - Blitzstein

High-School Resources

Book of Proof (Hammack)
Discrete Mathematics: An Open Introduction (Levin)
Calculus: Single Variable by Professor Robert Ghrist - video playlist
University of Waterloo Courseware for MHF and MCV
University of Cambridge - STEP Math Exam Preparation
University of Cambridge - STEP Math Exam Past Papers
University of Cambridge - STEP Support Program
NRICH Advanced Problem Solving Resources
Resources for Teaching A-Level Maths
University of Oxford - Maths Admissions Test
Math Competitions Compilation
Order of Operations - the 48/2(9+3) question
NZQA - New Zealand Qualifications Authority - Calculus Exams
MS Croggs Advent Calendar
Advent of Code - programming challenge
Chalkdust Magazine

LaTeX - Writing Papers in Mathematics and Using LaTeX

Online LateX Editor - Overleaf
Cartesian grid how-to: https://tex.stackexchange.com/questions/222882/drawing-minimal-xy-axis
- https://tex.stackexchange.com/questions/142120/positioning-of-pgfplot-axis-labels
- https://tex.stackexchange.com/questions/369929/label-pgfplot-axes-tikz
Presentation formats: beamer;
- Powerdot - a presentation class for latex
- Alternatives to beamer
PgfPlots.net - making graphs with LaTeX
PgfPlots Gallery - list of different graphs using pgfplots
Creating LaTeX commands
Math Symbols and Equations in Latex
The Not-So Short Introduction to Latex
TeXstudio - Latex Editor (all platforms)
Typing Exams in LateX
Detextify - draw a shape and get the LaTeX command for it
Overleaf - Collaborative online LaTeX editor
ShareLaTeX - Same as above
TeX Users Group
The Comprehensive TeX Archive Network
Art of Problem Solving Tutorial
TexPaste
Xfig
WriteLaTeX WYSIWYG
TeXample.net
The Comprehensive LaTeX Symbol List 338 page PDF with over 500 tables; when they say comprehensive, they mean comprehensive.

Graphs in LaTeX

TikZ Graph Examples
Graph examples - all types
Commutative Diagrams in TikZ
TikZ GUI editor
Minimal TikZ - pdf guide
gnuplot homepage
Demos for gnuplot version 5.2
matplotlib - Python graphing tool
Draw.io For scatterplots, flowcharts, etc.
MetaPost The MetaPost system implements a picture-drawing language that...outputs vector graphic files instead of run-length-encoded bitmaps; output formats available are PostScript and SVG.
Inkscape - draw program
SageMath Open Source Graphing Program
Asymptote - Vector Graphics Program
PSTricks - Gallery
Ipe extensible drawing editor
Free-hand graphing - can do with stylus and convert to latex
Clear basic steps to starting a cartesian graph
Grid-based diagram maker

Online Live Latex

MathB.in - Share mathematics on the web
LateX Base - Online Editor and Compiler

Tables in LaTeX

Tables Generator
Tables Editor
Controlling Table Columns in Latex

Math In Literature, or somewhat tangentially related

The Library of Babel - Borges
The Aleph - Borges
The Labyrinth - Borges
The Last Question - Asimov
The Nine Billion Names of God - Clarke
Mathematical Fiction - Chronological list

Problems

33 - Sum of cubes
42 is the new 33

Digital teaching presentation tools / resources:

Xournall ++ Note taking Software
Using phone as document camera setup
use Simple Screen Recorder to record work on screen
BigBlueButton - video conferencing
Jitsi - video conferencing

Proofs

How to Prove It - Velleman (full pdf)
Mathematical Expression and Reasoning for Computer Science
Proof Wiki
Math Counterexamples

Problem Solving

Problem Solving Repository

Extra Resources (taken from r/learnmath):

Khan Academy

PatrickJMT

Paul's Online Math Notes

Professor Leonard

MIT OCW

Better Explained

3Blue1Brown "Youtube channel that puts out fantastic videos intended to develop mathematical intuition, and motivating the subject. It includes possibly the best introduction to the subject of Linear Algebra I've ever come across. His calculus series is pretty great too. You should watch these in conjunction with the above resources."

Misc Advice: Math is not a spectator sport. Your brain learns by doing and practicing, not watching and reading. That means you need to do exercises. If you don't reinforce the lectures with problems you solve yourself, the knowledge will slip away over time. By the time you come back to it a month later, you'll have forgotten it all.

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Other Random Miscellany:

Open Source Mathematics Textbooks:

Open Textbook Library
Online Mathematics Textbooks
Linear Algebra - Jim Hefferon

Math Video Series

How to sum quadrillions of powers ... by hand! (Euler-Maclaurin formula - Mathologer)
Project Mathematics -The "Project MATHEMATICS!" video series explore basic topics in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. They bring mathematics to life with imaginative computer animation, live action, music, special effects, and a sense of humor. The videos were animated by James F. Blinn, and produced by Professor Tom M. Apostol at the California Institute of Technology, Caltech, in Pasadena, CA.
Calculus of Complex Variables, Differential Equations, and Linear Algebra: Herbert Gross (MIT Open Courseware) - View the complete course: http://ocw.mit.edu/RES18-008F11 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
Introduction to Linear Algebra - MIT OCW G.Strang

Learning and Studying Maths - Resources

Learning How to Learn: Powerful mental tools to help you master tough subjects
Learning How to Learn Seminar Series - Dan Wolczuk (Mathematics Faculty) with Student Success Office University of Waterloo
Mathematics Site - J.S. Milne
How to study for exams - Evidence-based revision tips

Word Counts - Big Data

Breaking Down Seinfeld

The constant e

Conceptualizing e - discussion

Emergence

Emergence - How stupid things bcome smart together

Inquiry Based Learning

Inquiry Based Learning?
Teaching Math Projects etc.
140 Challenge Levels Site

Pedagogy

Thinking Outside the Textbook

Bloom's Taxonomy Revised

Moving towards higher orders of thinking

Markov Processes

Markov Chains - explained visually
Really fast Markov chains in ~20 lines of sh, grep, cut and awk
Markov chains in Haskell