Secondary school Maths Book Series

Danica McKellar Maths books DeMYSTiFieD Maths Series Teach Yourself Maths Series For Dummies Maths Series Life of Fred Maths Series The Art of Problem Solving
Math Doesn’t Suck: How to Survive Middle School Math without Losing Your Mind or Breaking a Nail. Mathematics: A Complete Introduction: Teach Yourself by Hugh Neill Basic Maths For Dummies (UK Edition) by Colin Beveridge Life of Fred: Fractions &
Life of Fred: Decimals and Percents
Kiss My Math: Showing Pre-Algebra Who’s Boss. Pre-Algebra DeMYSTiFieD by Allan G. Bluman Basic Math & Pre-algebra For Dummies(R) by Mark Zegarelli Life of Fred: Pre-Algebra 0 Physics,
Life of Fred: Pre-Algebra 1 with Biology &
Life of Fred: Pre-Algebra 2 with Economics
Pre algebra by Richard Rusczyk, David Patrick, Ravi Boppana
Hot X: Algebra Exposed. Algebra DeMYSTiFieD by Rhonda Huettenmueller Algebra: A Complete Introduction: Teach Yourself by Hugh Neill Algebra I For Dummies by Mary Jane Sterling &
Algebra II For Dummies Mary Jane Sterling
Life of Fred: Beginning Algebra &
Life of Fred: Advanced Algebra
Algebra by Richard Rusczyk & Intermediate Algebra by Richard Rusczyk and Mathew Crawford
Girls Get Curves: Geometry Takes Shape. Geometry DeMYSTiFieD by Stan Gibilisco Geometry: A Complete Introduction: Teach Yourself by Hugh Neill Geometry For Dummies by Mark Ryan Life of Fred: Geometry Introduction to Geometry by Richard Rusczyk
Trigonometry Demystified by Stan Gibilisco Trigonometry: A Complete Introduction: Teach Yourself by Hugh Neill Trigonometry For Dummies(R) by Mary Jane Sterling Life of Fred: Trigonometry
Pre-Calculus For Dummies by PhD Yang Kuang Precalculus by Richard Rusczyk
Calculus Demystified by Rhonda Huettenmueller Calculus: A Complete Introduction: Teach Yourself by Hugh Neill Calculus For Dummies by Mark Ryan Life of Fred: Calculus Calculus by David Patrick
Secondary school Maths Book Series

English Literature Reading List

Wuthering Heights Emily Bronte
Sense and Sensibility Jane Austen
Cold Comfort Farm Stella Gibbons
Gulliver’s Travels Jonathon Swift
Jane Eyre Charlotte Bronte
Tess of the D’Urbervilles Thomas Hardy
Far from the Madding Crowd Thomas Hardy
A Picture of Dorian Gray Oscar Wilde
Silas Marner George Eliot
Frankenstein Mary Shelley
1984 George Orwell
Brave New World Aldous Huxley
Of Mice and Men John Steinbeck
The Grapes of Wrath John Steinbeck
The Outsider Albert Camus
The Kite Runner Khaled Hosseini
1000 Splendid Suns Khaled Hosseini
The Book Thief Marcus Zusak
Norwegian Wood Haruki Murakami
Enduring Love Ian McEwan
Atonement Ian McEwan
Catcher in the Rye J D Sallinger
Brighton Rock Graham Greene
Never Let Me Go Kazuo Ishiguro
Remains of the Day Kazuo Ishiguro
Falling Man Don DeLillo
Spies Michael Frayn
The Road Cormac McCarthy
Black Swan Green David Mitchell
If Nobody Speaks of Remarkable Things Jon McGregor To Kill a Mockingbird Harper Lee
White Teeth Zadie Smith
Wild Swans Jung Chang
Engleby Sebastian Faulks
Memoirs of a Geisha Arthur Golden
The Time Machine H G Wells
Sophie’s World Jostein Gaarder
Lovely Bones Alice Sebold
Purple Hibiscus – Chimamanda Ngozi Adichie

For a slightly lighter read…
Mister Pip – Lloyd Jones
Martyn Pyg – Kevin Brooks
The Woman in Black – Susan Hill
The King of the Castle – Susan Hill
Lord of the Flies – William Golding
The Hitchhiker’s Guide to the Galaxy – Douglas Adams His Dark Materials Trilogy – Phillip Pullman
Angela’s Ashes – Frank McCourt
Of Mice and Men – John Steinbeck
The Hound of the Baskervilles – Arthur Conan Doyle The Spy Who Came In From The Cold – John Le Carre Tales of The Otori (trilogy) – Lian Hearn
The Colour of Magic – Terry Pratchett
Slumdog Millionaire – Vikas Swarup
Fever Pitch – Nick Hornby


 

English Literature Reading List

Computer Science Readings

http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/readings/MIT6_042JF10_notes.pdf

http://www.saylor.org/majors/computer-science/
https://www.cybrary.it/
http://opensecuritytraining.info/Welcome.html

Linear algebra
Discrete mathematics

The C Programming Language Book by Brian Kernighan and Dennis Ritchie

Concrete Mathematics: Foundation for Computer Science by Ronald L. Graham, Donald E. Knuth and Oren Patashnik

Introduction to Algorithms Book by Charles E. Leiserson, Clifford Stein, Ronald Rivest, and Thomas H. Cormen

Art of Computer Programming, Volumes 1-4A Boxed Set, The By Donald E. Knuth

Computer Science Readings

Learning Resources for everyone

http://studygs.net
http://skillsyouneed.com

http://questioning.org/Q7/toolkit.html
http://socialresearchmethods.net/kb/index.php

http://thereasoner.org
http://kent.ac.uk/secl/researchcentres/reasoning/TheReasoner/contents.html

http://practicalmoneyskills.com
http://goodworkcommission.co.uk/Reports

http://brainpickings.org
http://theconversation.com/uk
http://tetw.org
http://edge.org
http://aeon.co

 

http://www.feynmanlectures.info

http://reddit.com
http://stackexchange.com
http://ask.metafilter.com
https://physicsforums.com
http://forums.welltrainedmind.com
https://quora.com

http://rationalwiki.org
http://lesswrong.com

http://www.linuxquestions.org
http://www.ubuntuforums.org
http://www.tomshardware.co.uk
http://www.tomsguide.com
http://www.techsupportforum.com
http://www.whirlpool.net.au
http://www.sevenforums.com
http://www.eightforums.com
http://www.tenforums.com

Learning Resources for everyone

Mathematic Readings

Algebra:
Algebra by I. Gelfand
Functions and graphs by I. Gelfand
The method of coordinates by I. Gelfand

Geometry:
Geometry: A High School Course by Serge Lang
Kiselev’s Geometry / Book I. Planimetry by A. P. Kiselev & Alexander Givental
Kiselev’s Geometry / Book II. Stereometry by A. P. Kiselev & Alexander Givental
Introduction to Geometry by H. S. M. Coxeter
Geometry Revisted by H.S.M. Coexter

Trigonometry:
Trigonometry by I.M. Gelfand

Pre-calculus:
Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by George F. Simmons

Calculus:
A First Course in Calculus by Serge Lang
Calculus and Analytic Geometry” by George Simmons

The Calculus Lifesaver: All the Tools You Need to Excel at Calculus by Adrian Banner
Calculus Made Easy by Silvanus P. Thompson

Calculus, Vol. 1 by Tom M. Apostol
Calculus by Michael Spivak
Calculus, Vol. 2 by Tom M. Apostol
Calculus On Manifolds by Michael Spivak

Problem Solving Books in Mathematic:
How to Think Like a Mathematician by Dr Kevin Houston
How to Prove It: A Structured Approach by Daniel J. Velleman
Problem-Solving Through Problems by Loren C Larson
How to Solve it by Polya
An Introduction to Mathematical Reasoning by Peter J Eccels
The Art and Craft of Problem Solving by Paul Zeitz
Problem-Solving Strategies (Problem Books in Mathematics) by Arthur Engel

Mathematical and Logic Puzzles:
The Lady or the Tiger?: and Other Logic Puzzles by Raymond M. Smullyan (age: 8 and up)
Entertaining Mathematical Puzzles by Martin Gardner (age: 10 and up)
My Best Mathematical and Logic Puzzles by Martin Gardner (age: 9 and 12)
Perplexing Puzzles and Tantalizing Teasers by Martin Gardner (age: 12 and up)
Alice in Puzzle-Land: A Carrollian Tale for Children Under Eighty by Raymond M. Smullyan (age: 80 and under)

Challenging Problems in Algebra by Alfred S. Posamentier (high school level)
Challenging Problems in Geometry by Alfred S. Posamentier (high school level)

Mathematical Puzzling by A. Gardiner (high school level)

Mathematical Puzzles: A Connoisseur’s Collection by Peter Winkler (high school, college, graduate level)
The Stanford Mathematics Problem Book: With Hints and Solutions by G. Polya (High school level)

Professor Povey’s Perplexing Problems: Pre-university Physics and Maths Puzzles with Solutions by Thomas Povey (College level)

Other masterpieces:
Alice in Wonderland by Lewis Carroll
Alice through the Looking Glass by Lewis Carroll
Alice Through the Needle’s Eye by Gilbert Adair
The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger (age: 10 and up)
Flatland by Edwin Abbott
A Mathematician’s Apology by G.H.Hardy
LockhartsLament by Paul Lockhart
The power of mathematics by Conway
Proofs from THE BOOK by Martin Aigner and Gunter Ziegler
Gödel, Escher and Bach: An Eternal Golden Braid by Douglas Hofstadter

Resources:
http://www.artofproblemsolving.com/store
http://math-blog.com/mathematics-books/
https://www.ocf.berkeley.edu/~abhishek/chicmath.htm
http://www.springer.com/series/3423
http://www.springer.com/series/136
http://www.springer.com/series/714
http://store.doverpublications.com/by-subject-mathematics.html

Mathematic Readings

Mathematic Resources

How to study mathematics by Paul Dawkins
http://tutorial.math.lamar.edu/pdf/How_To_Study_Math.pdf
http://tutorial.math.lamar.edu/Extras/StudyMath/HowToStudyMath.aspx

Study skills in mathematics
http://www.maths.cam.ac.uk/undergrad/studyskills/text.pdf

Common math error by Paul Dawkins
http://tutorial.math.lamar.edu/pdf/Common_Math_Errors.pdf
http://tutorial.math.lamar.edu/Extras/CommonErrors/CommonMathErrors.aspx

“How to Read Mathematics” by Shai Simonson and Fernando Gouvea http://web.stonehill.edu/compsci//History_Math/math-read.htm

Advice to a Young Mathematician
http://press.princeton.edu/chapters/gowers/gowers_VIII_6.pdf

Stewart, I., “How to Learn Math,” Letters to a Young Mathematician, Basic Books, 2006, pp. 62-70. (AMS Book Review)
This letter is from a wonderful collection of letters from a mathematician to “Meg,” as she progresses from a high school student wondering whether higher levels of math are anything more than “bigger numbers and harder calculations,” to a tenured professor. The letters are unerringly encouraging while explaining myriad aspects of what it’s like to be a mathematician. The letter, “How to Learn Math,” is to Meg when she is a college student and explains what to do to get past sticking points when reading. The author also advises Meg to “read around the subject” to gain a sense of the larger picture within which any subject fits.
https://archive.org/download/LettersToAYoungMathematician/ian_stewartLettersToAYoungMathematician.pdf

Terry Tao’s https://terrytao.wordpress.com/advice-on-writing-papers/

Gerver, R., “Reading and Keeping a Research Journal,” Writing Math Research Papers: A Guide for Students and Instructors Key Curriculum Press, 2004.
This book chapter provides guidance for reading the literature relevant to a research project. Subsections include “Preparing to Read,” “Reading and Taking Notes,” and “Conquering Difficult Concepts.”

How to Develop a Mindset for Math by Kalid Azad:
http://betterexplained.com/articles/how-to-develop-a-mindset-for-math/

Habits of Mind:
http://www.withoutgeometry.com/2010/09/habits-of-mind.html

Collection of math notes
http://www.maths.cam.ac.uk/studentreps/res/notes.html

Paul Dawkins online math notes
http://tutorial.math.lamar.edu/

Paul Dawkins cheet sheets: http://tutorial.math.lamar.edu/cheat_table.aspx
Harold’s Cheat Sheets: http://www.toomey.org/tutor/harolds_cheat_sheets.html
and other cheat sheets at http://cheatsheets.org

Math guy handbook: http://www.mathguy.us/
Colecao Schaum’s (mathematical – formulas and tables)
http://florida.theorangegrove.org/og/file/3a8c652c-11d0-e967-95fb-b5bbae2586d6/1/math_handbook.pdf
Handbook for spoken mathematics Lawrence Cheng PhD

First steps in algebra by George Albert Wentworth
Beginning and intermediate algebra by Tyler wallance

Advanced high school mathematics by David b. Surowski
Fundament Concepts of Algebra
Trigonometric delights Eli Maor

PreCalculus by Carl Stitz and Jeff Zeager
PreCalculus an investigation of functions by David Lippman and Melonie Rasmussen
Funny Little Calculus Text by Robert Christ

How do undergraduates do mathematics? A guide to studying mathematics at Oxford University Charles Batty St. John’s College, Oxford
https://www0.maths.ox.ac.uk/system/files/study-guide/guide.pdf

Preparing for university calculus prepared by apics committee on mathematics and statistics edited by Robert Dawson
http://cs.smu.ca/apics/calculus/CalcPrep1.pdf

Advanced problems in core mathematics by Stephen siklos
http://www.maths.cam.ac.uk/undergrad/admissions/step/advpcm.pdf

Undergraduate Mathematics Reading List
http://www.maths.cam.ac.uk/undergrad/admissions/readinglist.pdf

Introduction to logic by Harry J. Gensler
Mathematical Reasoning writing and proof by Ted Sundstorm
Language proof and logic by Jon Barwise & John Etchemendy
Fundament Concepts of Mathematics
Book of proof by Richard Hammack

Websites:
https://reddit.com/r/math/comments/2mkmk0/a_compilation_of_useful_free_online_math_resources
http://khanacademy.org
http://artofproblemsolving.com
http://learner.org/courses/mathilluminated/
http://world.mathigon.org
http://betterexplained.com
http://www.artofmathematics.org
http://mathpuzzle.com
http://mathworld.wolfram.com
https://reddit.com/r/puremathematics
http://math.stackexchange.com
http://mathoverflow.net
http://mathinsight.org
http://proofwiki.org/wiki/Main_Page
http://encyclopediaofmath.org
https://oeis.org
http://arxiv.org
http://ams.org/notices
http://plus.maths.org

Mathematic Resources

How does the stock market work?

Answer by Balaji Viswanathan:

TL;DR: "In the short term, the market is a voting machine. But, in the long term, the market is a weighing machine".  — Ben Graham[1]
Part 1: How the stock market works
Part 2: How does one evaluate Stocks

Part 1: Basics of a Stock Market
History: A long  time ago, humans ran businesses with just their money. The businesses  they ran were small and they grew the businesses only with their own  profits. However, not all businesses can be built with your own money.  What if you wanted to build a new factory that costs more than a million dollars? Banks won't lend money for young companies and your friends won't have that much.

In the 15th-16th century as the Europeans started exploring Asia and Americas, the big explorers felt they needed a lot of money and their kings were not providing them anymore. The wealthy guys demanded a lot of interest. Thus, they felt they need to raise money from a bunch of common people. Thus, in 1602, the Dutch East Indian company became the first company to issue shares of its company in the Amsterdam Stock Exchange and get traded on a continuous basis.

What is a Stock? Stocks  in a company provide you a share of the company's future profits in  return for the capital invested. For instance, if you buy 1 stock of  Apple now, you will be assured one-billionth of  Apple's profits in the  future (as there are almost a billion such stocks that Apple has issued  now).

Listing: In  a stock market, 1000s of companies are listed and these companies  (called public companies – as they have given out their shares to common  public) pay a fee to the exchanges, along with a promise to provide all  important info to the markets. In return they get an opportunity to put  their company in the stock market's board & have the ability to get  money from people visiting the market. The first time a company's stock  appears on the stock market's board is called an IPO (Initial Public Offer).

Brokers: Conceptually,  a stock exchange is similar to eBay. These guys allow companies to  be listed and connect the buyers & sellers. Since millions of people  trade in the market and it is practically impossible for these  exchanges to deal with all the individuals, they have assigned brokers who act between the exchanges and the individuals.

Part 2: How does one value a stock
Basic Terminology:
We will use a term EPS (Earnings per share) that is exactly as it sounds. It is the profits of the company divided by number of shares. For instance, Apple has $41 billion in profits and about 950 million shares, giving an EPS of about 41000/950 = $44/share. Thus, if you own a share of Apple, you are entitled to 44 bucks of Apple's profits this year.

Calculating Share price:
To evaluate how much you need to pay for that 1 Apple stock you need to do a simple addition of all the earnings you will get

         Stock Price = EPS in Year 1 + EPS in Year 2 +…

Now, you know that a dollar earned 10 years from now is not the same as a dollar earned now. Because, there is an interest rate i involved and money you get in 10 years is less worthy than the money you have now. Thus, you need to adjust that formulae.

        Stock Price = ((EPS in Year 1)/(1+i))+ (EPS in Year 2/(1+i)^2) +…

Now, there is a whole bunch of math involved (starting from the compound interest formula) and for the sake of simplicity, I will get you to the final results and reduce the stock price to two cases:

1. In case of a mature company that doesn't grow:
          Stock price = EPS/Interest rate

The expected Interest rate is relatively easy to calculate and depends on how risky the company is, how risky the market is and the current long term interest rate of government bonds. For many mature utility companies this interest rate comes to about 10%. Thus, utility companies that doesn't grow much is generally traded at about 10-15 times the EPS. (insert in the formula above).

The stock prices of these companies are very smooth and change only when there is a change in long term interest rates, the risk profile of the company (can change when hurricanes such as Sandy hits) or when market risk changes (for instance 2008 financial crisis). But on a regular day, not much action here. Let us move to the second category of shares:

2. For a growing company:
           Stock price = EPS of next year / (interest rate – expected growth rate of the company)

Let us use a simple example. If you assume Apple's next year EPS will be $48, the expected interest rate for such a risky company at 15% and an expected annual growth rate at 5%, you will get:

$48/(15%-5%) or $48/10% or $480 as the ideal stock price for the company. Where did I get this magical 5% number?

Getting the growth inputs:
Now, we need to find the growth rate of the company and figure out what the company will earn in the next year, the following year and so on. This is not an exact science and no one has a perfect answer to this question. This is why we need stock markets. Collectively, we all pool our intelligence to figure out the future growth of the company and thereby its current price.

To do this collective prediction, we constantly get new inputs and project that to future. For instance, if the company management gets hotshot new engineers, then we predict the future will be bright. What are the other news that investors typically use:

  1. Periodic financial results of the company that gives us a view into the company;s workings and its financial position
  2. Periodic results of similar companies that helps us guess this company;s results. Thus, when Apple sneezes everyone else catches a cold.
  3. Changes in the sector. If a new report comes that people are more inclined to using mobile phones, we predict growth of these companies will be high.
  4. Changes in the broader market.
  5. Changes in the international economy

Market Estimation:
In short, we try to use every possible information to guess the future growth of the company, plug that into our formula and find out the stock price. For instance, if Apple comes out a report saying people are buying less of iPads, we might ding Samsung too as we believe their Galaxy Tabs will sell less too.

Estimating growth rate is an art rather than a science, and is collectively done by millions of humans in a place called the stock market. Since, we need to constantly adjust the growth rate based on new information, stock prices constantly fluctuate.

Main advantages of a stock market:
1.  Starting/building a business: The market lets companies get money from a large number of people. That means there are more options to get money to build a business.

2.  Spreading risk: It lets you spread the risk of a business into a large  number of people. Since, each person is investing only a small portion  of their income in the stock of a particular company, the risk of a single company collapsing doesn't significantly affect investors.

3. Collective estimation of value.
 
Summary: Modern corporations require a lot of capital, which is beyond the reaches of a few individuals. Markets help companies raise money from a large number of  people and together these investors value their company. The theory is  that when a large number of people do their independent valuation, the  company's price comes more closer to its ideal worth.

 "In the short term, the market is a voting machine. But, in the long term, the market is a weighing machine".  — Buffett

(Disclaimer: This is an answer targeted at basic-intermediate level investor & not high frequency traders or experts. I deliberately approximated a few things to improve clarity).
[1] Buffett's metric says it's time to buy

Balaji Viswanathan's answer to What should everyone know about investing?
Balaji Viswanathan's answer to What should everyone know about economics?

How does the stock market work?

How does the stock market work?