Category Archives: Mathematics

Course in Mathematics

July 1, 2016 – 12:41 PM
Remedial

Reference: Course on Subject Clearing

The Book of Mathematics
Troubleshooting Math

Earlier Gradients

  1. Pre-algebra (Khan Academy)
  2. Algebra 1 (Khan Academy)
  3. Algebra 2 (Khan Academy)

SAT Prep

  1. Algebra Review
  2. Word Problem Review
  3. Practice Problems
  4. PSAT & SAT Review
  5. SAT Math (Khan Academy)

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REFERENCES

Arithmetic

  1. Combinations and Permutations
  2. 1885 Ray’s Practical Arithmetic
  3. 1893 Dubb’s Arithmetical Problems

Algebra

  1. Algebra Cheat Sheet (reduced)
  2. Algebra Cheat Sheet (full)
  3. Synthetic Division
  4. Vertical and Horizontal Asymptotes
  5. Matching Polynomials with Graphs
  6. Inequality Problem
  7. Old Algebra Book
  8. Paul’s Online Math Notes (Algebra)
  9. 1895 Coordinate Geometry (S L Loney)

Geometry

  1. Point and Unit
  2. Geometry—all content (Khan Academy)
  3. Analytic Geometry—all content (Khan Academy)
  4. High school geometry (Khan Academy)
  5. Old Geometry Book
  6. Euclid’s ELEMENTS
  7. Math Pages (Geometry)

Trigonometry

  1. Trigonometry Cheat Sheet (full)
  2. Trigonometry Cheat Sheet (reduced)
  3. Trigonometry Index
  4. Trigonometry (Khan Academy)
  5. Paul’s Online Math Notes (Trigonometry)
  6. 1915 Plane Trigonometry (S L Loney)

Calculus

  1. Calculus Cheat Sheet
  2. Paul’s Online Math Notes
    1. Calculus I
    2. Calculus II
    3. Calculus III
    4. Differential Equations
  3. Volumes by Cylindrical Shells
  4. Triple Integrals, Changing the Order of Integration, Part 1 of 3
  5. Double Integrals – Changing Order of Integration
  6. Triple Integrals, Changing the Order of Integration, Part 2 of 3
  7. Triple Integrals, Changing the Order of Integration, Part 3 of 3
  8. HMC Online Tutorials
  9. Math Pages

Statistics

  1. Statistics Online
  2. Math Pages
  3. Mean, Median, Mode and Range
  4. Quartiles, Boxes, and Whiskers
  5. Five-number summary
  6. Interquartile ranges and outliers
  7. Standard Deviation

General References

  1. Some Old Books
  2. Purple Math
  3. Common Core Math Standards

ESSAYS

  1. The Abacus and Numbers
  2. Numbers & Consciousness
  3. Going Beyond Counting
  4. Point and Unit
  5. Infinity and Unknowable
  6. Comments on Infinity
  7. Math Homonyms
  8. Math Imitating Life
  9. The Algebra of Unknowable
  10. Fundamentals, Consistency and Breakthroughs
  11. A Musical Interpretation of Pi

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By vinaire | Comments (9)

Discrete and Continuous

February 6, 2015 – 9:52 AM

VLT image of the cometary globule CG4

A rational number, whether real, imaginary or complex is a discrete entity. A discrete entity has a boundary of value. A set of discrete entities is a collection of such values with boundaries.

A scale, dimension, or field is a continuous entity that is stretched out. A continuous entity has continuously varying values. There is no boundary that defines an exact value.

The moment you refer to a “number” you have placed a boundary around a value by identifying it.

A continuous scale, dimension, or field may be filled with a lot of precisely defined numbers, but these numbers remain separate from the scale.

When you say, “There is a continuous field of numbers,” all you are saying is that there is a continuous field that may be filled with numbers. That continuous field is still there when it is not filled with numbers. The numbers DO NOT MAKE the field.

There are no precisely identifiable irrational numbers. When one is looking at an irrational number one is looking at a piece of scale, dimension, or field.

A continuous function like SINE is by itself. It is not made up of numbers, though infinity of numbers may fit into any segment of it.

The bottom line is,

“INFINITY OF DISCRETE ENTITIES DO NOT TOGETHER MAKE A SINGLE CONTINUOUS ENTITY.”

Space may be filled with points; but space is not the same thing as a set of points.

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By vinaire | Also posted in Science | Comments (46)

PSAT / SAT Prep

August 4, 2014 – 8:51 AM
Filling in bubble test
Reference: Maths Self Learning

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WORD PROBLEMS REVIEW

300: 01 Simple Equation Problems

310: 02 Percent Problems

320: 03 Advanced Level Age Problems

330: 04 Mixing Problems

340: 05 Measurement (Ratio) Problems

350: 06 Rate Problems

360: 07 Statistics & Probability

370: 08 Geometry Problems

380: 09 Review of Equations

390: 10 Answers to Practice Problems

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PSAT & SAT REVIEW

400: 01 PSAT Diagnostics 1

405: 02 PSAT Diagnostics 2

410: 03 PSAT Algebra

420: 04 PSAT Equation

430: 05 PSAT Inequalities

440: 06 PSAT Geometry

450: 07 PSAT Fractions

460: 08 PSAT Percentage

470: 09 PSAT Averages

480: 10 PSAT Rates

490: 11 PSAT Ratio

500: 12 PSAT Work

510: 13 PSAT Data Interpretation

520: 14 PSAT Quantitative Comparison

530: 15 PSAT Typical Test A

540: 16 PSAT Typical Test B

550: 17  PSAT Typical Test C

560: 18 PSAT Typical Test D

570: 19 PSAT Typical Test E

580: 20 PSAT Typical Test F

590: 21 PSAT Typical Test G

600: 22 PSAT Typical Test H

610: 23 PSAT Typical Test I

620: 24 PSAT Typical Test J

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PRACTICE PROBLEMS

There are hundreds of sets of excellent practice problems in 465. Some of the sets are listed from 651.

651: SET1001 / Solutions

652: SET1002 / Solutions

653: SET1003 / Solutions

654: SET1004 / Solutions

655: SET1005 / Solutions

656: SET1006 / Solutions

657: SET1007 / Solutions

658: SET1008 / Solutions

659: SET1009 / Solutions

660: SET1010 / Solutions

661: SET1011 / Solutions

662: SET1012 / Solutions

663: SET1013 / Solutions

664: SET1014 / Solutions

665: MATHDEN (User ID: guest; Password: guest)

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By vinaire | Comments (2)

Pre-Algebra Review

August 3, 2014 – 8:25 PM
Pre-Algebra
Reference: Maths Self Learning

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PRE-ALGEBRA – BASICS

PA 100: Natural and Whole Numbers

PA 101: Math Homonyms

PA 102: Concepts in Arithmetic (1)

PA 103: Concepts in Arithmetic (2)

PA 104: Arithmetic Overview

PA 105: Math Overview

PA 106: Equations & Transposition

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PRE-ALGEBRA – REVIEW

PA 100: Diagnostics

PA 110: UNIT  01 Real Numbers / Answers to Unit 01

PA 120: UNIT  02 Variable Expressions / Answers to Unit 02

PA 130: UNIT  03 Solving Equations / Answers to Unit 03

PA 140: UNIT  04 Solving Equations: Applications / Answers to Unit 04

PA 150: UNIT  05 Polynomials / Answers to Unit 05

PA 160: UNIT  06 Factoring / Answers to Unit 06

PA 170: UNIT  07 Algebraic Functions / Answers to Unit 7

PA 180: UNIT  08 Graphs & Linear Equations / Answers to Unit 08

PA 190: UNIT  09 Systems of Linear Equations / Answers to Unit 09

PA 200: UNIT  10 Inequalities / Answers to Unit 10

PA 210: UNIT  11 Radical Expressions / Answers to Unit 11

PA 220: UNIT  12 Quadratic Equations / Answers to Unit 12

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By vinaire | Comments (0)

Middle School Math Review

July 7, 2014 – 10:23 AM

Middle School

 

MIXED OPERATIONS REVIEW

Reference: MILESTONE 6: Mixed Operations

Review 50: Order of Operations

Review 51: Addition and Subtraction

Review 52: Multiplication and Division

Review 53: Expression and Terms

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INTEGERS REVIEW

Reference: MILESTONE 7: Integers

Review 60: Integers, What They Are

Review 61: Sign and Absolute Value

Review 62: Counting with Integers

Review 63: Multiplying & Dividing Integers

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FACTORS REVIEW

Reference: MILESTONE 8: Factors

Review 70: Factors, What They are

Review 71: Single-Digit Prime Numbers

Review 72: Double-Digit Prime Numbers

Review 73: Prime Factors of a Number

Review 74: Prime Factors Divisibility

Review 75: Division by Factoring

Review 76: Greatest Common Factor

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FRACTIONS REVIEW

References: MILESTONE 9: Fractions (Part I) / MILESTONE 10: Fractions (Part II)

Review 80: Fractions, What They Are

Review 81: Unit Fractions and Multiples

Review 82: Proper and Improper Fractions

Review 83: Mixed Numbers

Review 84: Equivalent Fractions

Review 85: Comparing Fractions

Review 86: Least Common Multiple

Review 87: Addition &Subtraction

Review 88: Multiplication & Division

Review 89: Mixed Operations

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DECIMAL NUMBERS REVIEW

Reference: MILESTONE 11: Decimal Numbers

Review 90: The Decimal System

Review 91: Decimal Numbers

Review 92: Decimal Fractions

Review 93: Decimal and Common Fractions

Review 94: Decimal Addition & Subtraction

Review 95: Decimal Multiplication & Division

Review 96: Periodic or Repeating Decimals

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By vinaire | Comments (0)