Vectors and Matrices are important especially in fields like Machine Learning , Data Science , Image Processing, Computer Graphics
This principle is simple. Look at falling dominoes herehttp://en.wikipedia.org/wiki/Mathematical_induction. The inductive step is important. If some statement holds true for number N implies that it holds true for N+1, it follows that the statement holds true for every number.
Looks simple ? Ready for some advanced exercises ?http://server.math.uoc.gr/~tzanakis/Courses/NumberTheory/MathInduction.pdf
Pigeon Hole Principle
What is the relationship between Hashtables, Pigeonholes, and Birthdays
Pigeon hole principle looks very simple- If you try to put 6 pigeons in 5 holes, one will inevitably be left out.
But its applications are varied. For example, this birthday problem and also in finding collisions in hashtables
In a typical classroom of 30 students, what are the odds that two of the students will have the same birthday?
Originated by Euler’s method to determine whether crossing 7 bridges exactly once possible. Has wonderful applications.
Look here for list of applications of graph theory http://jwilson.coe.uga.edu/emat6680/yamaguchi/emat6690/essay1/gt.html?dhiti=1
See http://eprints.nuim.ie/2702/1/FO_Mathematics.pdf for such beautiful proofs including ones by Gauss
Mathematics for Computer Science
Prof.Leighton at MIT (founder of Akamai ) explains the basics of mathematics – Induction, Number theory, Modular arithmetic
The examples are engaging. For e.g, one is from a movie – Bruce is given a 3-gallon jug and a 6-gallon jug and must
measure out exactly 4 gallons. They also explain how number theory principles are used for securing your data – namely the foundations of RSA cryptography. They give nice and practical examples where graphs are used to model
Generating functions http://math.mit.edu/~goemans/18310S15/generating-function-notes.pdf
Article – Permutations and Combination
Mathematics for Algorithm analysis
Analysis of algorithms is explained by Peteris
It points to lecture by Erik Demaine. The second half of the lecture is devoted to solving recurrence equations. Three methods are presented:
Recursion-tree method, and
The Master method.
Mathematics for Programmers
How much mathematics should a programmer know. What is the right way to learn math. Steve Yegge writes here
Knowing even a little of the right kinds of math can enable you do write some pretty interesting programs that would otherwise be too hard. Nobody knows all of math, not even the best mathematicians.
Khan’s Academy videos on Probability / Linear Algebra