Mathematics

NUMBERS

1. Division by 0
2. Rational and Irrational Numbers
3. Counting the Infinite: A Glimpse at Infinite Sets
4. Is 0.999… really equal to 1?
5. Prime Series 1: Introduction to Prime Numbers
6. Prime Series 2: The Intuition Behind the Infinitude of Primes
7. Prime Series 3: Proof of the Infinitude of Primes
8. Making Sense of Exponential Growth
9. Counting the Real Numbers
10. Young Gauss and the Sum of the First n Positive Integers
11. Dominoes and Mathematical Induction
12. Pythagorean Triple 1: The Infinitude of Pythagorean Triples
13. Pythagorean Triple 2: Generating Pythagorean Triples
14. Large Numbers and One Million
15. Light Year and the Mathematics of the Stars
16. The Geometry of Commutativity
17. The Distributive Property
18. The Commutativity of Real Numbers
19. Military Drills and the Closure Property of Real Numbers
20. Finger Math 1: Finger Multiplication
21. Finger Math 2: Why Finger Multiplication Works
22. Understanding Fermat’s Last Theorem
23. Irrational Numbers as Decimals
24. Order of Operations: 360 or 354?
25. The mysterious 495
26. The mystery of 495 exlpained
27. The Golden Ratio
28. The Kaprekar constant 6714
29. Operations on Integers – Addition
30. Operations on Integers – Subtraction
31. Operations on Integers – Discovering multiplication and division of integers using patterns
32. Real Numbers: A summary
33. Is 0 a natural number?
34. Multiplication of Fractions
35. Linking sum of counting numbers to triangle area
36. Pi to 10 Trillion Digits
37. Using Area to Prove the Arithmetic Mean-Geometric Mean Inequality
38. Another Proof of the Sum of the First n Positive Integers

Complex Numbers Series

1. What is i? What are imaginary numbers?
2. Complex Numbers and Their Properties
3. Demystifying Complex Conjugates
4. Introduction to the Complex Plane

 The Divisibility Series

• Divisibility by 2
• Divisibility by 4
• Divisibility by 5 and 10
• Divisibility by 3
• Divisibility by 7 and its Proof
• Divisibility by  8
• Divisibility by 9

ALGEBRA

1. Making Connection Between Distance and Absolute Value
2. Letters, Variables and Algebraic Expressions
3. Matchsticks, Linear Relations, and Multiple Representations
4. Equation of a line: The derivation of y = mx + b
5. Slope Concept 1 – Understanding the Basic Concepts of Slope
6. Slope Concept 2 – Slope of the Graph of a Linear Function
7. Slope Concept 3 – Slopes of Vertical and Horizontal Lines
8. Arithmetic Sequences and Linear Functions
9. Derivation of the Quadratic Formula
10. Understanding the Meaning of Discriminant
11. Geometric Sequences and Series
12. Why do we reverse the inequality sign?
13. Why is any number raised to 0 equals 1?
14. Why is zero factorial equals 1?
15. How to use the summation symbol
16. Compound Interest and the Irrational Number e
17. Functions 1: Introduction to the Concept of Functions
18. Functions 2: Basic Concepts of Functions
19. Vectors, Parallelograms and Commutativity
20. Simon’s Favorite Factoring Trick
21. Addition of Coordinates
22. The Handshake Problem and Its Multiple Solutions
23. The Multiplication Parabola
24. Mathematical Equations and Their Properties
25. The 12 days of Christmaths and the Triangular Numbers

GEOMETRY

1. Chess and Axiomatic Systems
2. Angle Sum of Polygons
3. Why is the angle sum of the interior angles of a triangle equal to 180 degrees?
4. Parallel Lines and Transversals
5. The Exterior Angle Theorem
6. Is there an SSA Congruence?
7. Making Connections among Pythagorean Theorem, Distance Formula and Equation of a Circle.
8. The Algebraic and Geometric Proof of Pythagorean Theorem
9. Tessellation: The Mathematics of Tiling
10. Is a square a rectangle?
11. The Inscribed Angle Theorem
12. Demystifying Triangle Inequality
13. Constructing Segments with Irrational Lengths
14. Similarity 1: Introduction to Similarity
15. Similarity 2: Properties of Similar Triangles 1
16. Similarity 3: Properties of Similar Triangles Part 2
17. A Closer Look at the Midpoint Formula
18. Eratosthenes and the Earth’s Circumference
19. Platonic Solids: Why only five of them?
20. Regular Tessellations: Why only three of them?
21. The Seven Bridges of Konigsberg
22. Discovering Properties of Parallelograms
23. The Marvels of the Nine-Point Circle
24. Introduction to Coordinate Geometry
25. Undefined terms: What are they?
26. Diagonals of a Parallelogram
27. A US President’s Proof of the Pythagorean Theorem

Area Tutorial Series

1. Area Tutorial 1 - Introduction to the Concept of Area
2. Area Tutorial 2 – Area of a Triangle
3. Area Tutorial 3 – Area of a Parallelogram
4. Area Tutorial 4 – Area of a Circle
5. Area Tutorial 5 – Area of a Trapezoid

TRIGONOMETRY AND PRECALCULUS

1. Demystifying Degree and Radian Measures
2. An elementary proof of the cosine law
3. Folding a Hyperbola
4. The Complements Theorem
5. Pi and the Circle
6. Jeepneys and Step Functions
7. The Proof of the Tangent Half-Angle Formula

CALCULUS

1. An Intituive Introduction to Limits
2. An extensive explanation about the  definition of limits
3. Limit by  proof: Example 1
4. Limit by proof: Example 2
5. Derivative Concept 1: The Algebraic and Geometric Meaning of Derivative
6. Derivative Concept 2: Derivative in Real Life Context
7. Derivative Concept 3: Derivative and the Maximum Area Problem

STATISTICS, PROBABILITY AND COMBINATORICS

1. Introduction to Permutations
2. Introduction to Combinations
3. Binomial Theorem Series 1: Milkshakes, Beads, and Pascal’s Triangle
4. Binomial Theorem Series 2: The Binomial Expansion
5. A Gentle Introduction to Probability
6. The Unfinished Game Problem
7. Using Mathematics to Win the Lottery
8. Storytelling and Statistics at their finest
9. Ben Goldacre and Bad Statistics
10. Understanding the Multiplication Principle
11. Probability Terminologies and Notations
12. Wedding Guests and Circular Permutations

PROOFS

1. Proof Tutorial 1: Introduction to Mathematical Proofs
2. Proof Tutorial 2: Proving the Irrationality of Square Root of 2 by  Contradiction
3. More examples of Proof by Contradiction
4. Proof that log 2 is irrational
5. Proof by Contradiction: Knights and Liars

MATH LITE

1. Funny Math – 10 Steps you Need to Solve a Calculus Problem
2. The Square Root of Three
3. Why Mathematics Teachers Drink Part 1
4. Why Mathematics Teachers Drink Part 2
5. Men, Women, and Mathematics
6. Amazing Number Patterns
7. Simba sings math
8. Math is …
9. Nature by Numbers: Watch and fall in love with math
10. Potato chips and mathematics
11. Math Easter Egg
12. Calculus Rhapsody
13. Three
14. Math Words in Filipino
15. Calculating the volume of a pizza
16. Math, Santa and Venn Diagrams
17. Tangled and the Mathematics of Hairdressing
18. The Beauty of Narcissistic Numbers
19. Heart Graph for the Mathematically In Love
20. Would you have given a different mark?
21. Why Every Proof that 0.999… = 1 is Wrong
22. Mathematics and Perspective

MISCELLANEOUS

Vedic Mathematics (by Sanjay Gulati)

1. Introduction to Vedic Mathematics
   
2. Squaring Numbers in 5
3. Multiplication with a series of 9s
4. Nikhilam Method of Multiplication
5. Nikhilam Method of Multiplication 2
6. Squaring Numbers: Part 1

Paper Folding

1. Getting the square root of any  number on a number line
2. Paper Folding: Extracting the cube root of a number
3. Paper Folding: The proof of the cube root applet
4. Origami and GeoGebra — a slightly different version

Set Theory

1. Sets: A Gentle Introduction
2. Subset: A set contained in a set
3. Sets: Terminologies,  Notations, and Operations
4. Counting the Number of Subsets in a Set

Others

1. The Mystery Behind the Proof of 1 = 2
2. The Search for Magic Squares
3. The definition of Undefined
4. Is mathematics and exact science?
5. Steven Strogatz
6. Making Mathematicians I
7. How do mathematicians greet happy valentines?
8. SOMEBODY up there pushed me
9. Would you have made it into Harvard in 1869?
10. All time Top Mathematics Posts
11. A Hundred Years Down the Road
12. The man who conned a mathematician
13. 10 Ways to Think Like a Mathematician
14. Applying Mathematics to Web Design
15. Mathematics and the Love of God?
16. 25 Signs You’re a Future Mathematician
17. Who Owns the Zebra?
18. Lottery Math — If you play, you should know your odds
19. The Mathematics of Leap Years Explained

MATH RESOURCES/FREEBIES

1. More than 20,000 contest problems and solutions
2. 8000+ Math, Physics, and Engineering applets
3. Calculus 1 Video Lectures
4. 8 Free Online Graphing Tools

MATH TEACHING AND PEDAGOGY

1. Math Exercise, Problem Solving, and Investigation
2. The Inverted Classroom
3. Conrad Wolfram: Teaching kids real math with computers
4. When do mathematical definitions matter?
5. Exploring Computational Thinking
6. Math Curriculum Makeover
7. What is Universal Design Learning
8. Popularizing Lesson Study
9. Using Paper Folding to Introduce the Notion of Proof
10. 10 Tips in Studying School Mathematics
11. Constructing Open -Ended Math Problems