Basic Concepts in Math and Science - a complement to school texts
Kerman Bharucha
Apex NC (USA)
Table of Contents:
Introduction:
Section 1: Point, Line, Straight Line, and the True Meaning of Numbers; Defining point, line, straight line; The true meaning of numbers; The all-important number axis; Positive and negative numbers; Smaller and larger numbers; Some logical thinking with numbers; Numbers 1 through 100.
Section 2: Larger Numbers; Numbers 101 to 999; Units, tens, hundreds and place value; Verbalizing hundreds, thousands, millions, billions and beyond.....; Writing out hundreds, thousands, millions, billions and beyond.....
Section 3: Addition and Subtraction; Addition; Addition involving negative numbers; Addition for the real world; Basic addition word problems; Can you prove that 1 + 1 = 2?; Subtraction; Subtraction involving negative numbers; Subtraction for the real world; Subtraction leading to a negative answer; Direct subtraction leading to a negative answer; The "decomposition" subtraction algorithm followed in the USA; Basic subtraction word problems.
Section 4: Multiplication; Multiplication for the real world; Multiplication by 10; Fast multiplication involving ½ ; Multiplication involving negative numbers ; Basic multiplication word problems; The Matrix.
Section 5: Division; Division for the real world; Division involving negative numbers; Long division; Divisibility rules; Basic division word problems.
Section 6: Multiples and Factors; Multiples; Factors.
Section 7: Prime Factorization; Even, odd and prime numbers; Prime factorization; Prime factorization using "Tree" diagrams.
Section 8: Fractions; Proper fractions; Improper fractions; Negative fractions; Reducing fractions; Adding fractions; Subtracting fractions; Comparing fractions; Multiplying fractions; Dividing fractions; Reviewing cross-multiplication in fractions; Verbalizing fractions; Improper fractions and mixed numbers.
Section 9: Ratios, Distributions, Equivalency of Ratios; Explaining ratios; Doing the distribution; The math behind distributions based on ratios; The connection between distribution ratios and fractions; The equivalency of ratios.
Section 10: Exponents (Squares, Cubes, etc.) and Roots; Squares and cubes, etc.; Roots; Fractional indexes.
Section 11: Absolute value (or Modulus); Emphasizing the connection between (a-b) and (b-a); Absolute value (or modulus).
Section 12: Math Expressions; Math expressions; Reducing / simplifying Math expressions.
Section 13: Decimals; The decimal point; Addition with decimals; Subtraction with decimals; Multiplication with decimals; Division with decimals; Dividing decimal numbers by 10, 100, 1000; Writing out large numbers with decimals.
Section 14: Other Number Systems; A Martian visits; Converting numbers between number-systems; The Martian returns.
Section 15: Conversions: Decimals â" Fractions â" Percentages; Fast percentage calculations; Expressing increases and decreases in fractions and percentages.
Section 16: Classification of Numbers.
Section 17: Rounding and Scientific Notation.
Section 18: Permutations and Combinations.
Section 19: The Balance Concept in Math - crucial!; The basics of the balance concept; Balances as fractions - very useful!.
Section 20: Unit and Dimension Analysis and Conversion; Areas and Volumes.
Section 21: Some Interesting Mental Math; Squares and products of larger numbers; Fast multiplication by 11.
Section 22: Basic Algebra (quite detailed).
Section 23: Basic Geometry (quite detailed).
Section 24: Basic Coordinate Geometry (quite detailed).
Section 25: Basic Science Concepts.
