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Mathematics Dictionary
Algebra

Subjects

  • AL 00 | - Tips
  • AL 01 | - Axioms and Laws
  • AL 02 | - Polynomials and Functions
  • AL 03 | - Numbers
  • AL 04 | - Linear functions
  • AL 05 | - Quadratic Functions
  • AL 06 | - Exponent laws
  • AL 07 | - Binomial Theorem
  • AL 08 | - Series
  • AL 09 | - Logarithm
  • AL 10 | - Partial Fraction
  • AL 11 | - Equations and Inequality
  • AL 12 | - Complex Numbers
  • AL 13 | - Matrix and Derterminant
  • AL 14 | - Mathematical Induction
  • AL 15 | - In-equalities
  • AL 16 | - Rational function
  • AL 17 | - Probability
  • AL 18 | - DeMoivre's theory
  • AL 19 | - Indefinite equations
  • AL 20 | - Algebra Index
  • AL 21 | - Graphs of y = F(x) in algebra
  • AL 22 | - Glossay
  • AL 23 | - Home Work
  • AL 24 | - References and examples
  • AL 25 | - Examples : Questions in alphabetic orderReferences and examples
  • AL 26 | - Algebra formulae
  • AL 27 | - Examples with solutions
    • Answers


    AL 01. Axioms and Laws


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    AL 02. Polynomials and Functions

    • Topic | Polynomials and Functions
    • Example : Polynomial addition and multiplication
    • Example : Various names of functions
    • Example : Sketch curves of functions
      • Sketch y = F(x).
      • Sketch y = F(x)/G(x).

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    AL 03. Numbers

    • Topic | Numbers : Defintion and properties
    • Examples
      • How to find the 3rd perfect number ?
      • Amicable pairs are 1184 and n. Find n.

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    AL 04. Linear Functions

    • Topic | Linear Functions : y = a*x + b.
    • Outlines
      • 1. Properties of linear functions
      • 2. Study function with absolute operations
      • 3. Study inverse functions

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    AL 05. Quadratic Functions

    • Topic | Quadratic Functions : y = a*x^2 + b*x + c.
    • Example : Absolute operation : y = |a*x^2 + b*x + c|.
    • Example : Inverse functions
    • Example : Parabola
    • Example : Vertex expression y - yv = a*(x - xv)^2.

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    AL 06. Exponent and Logarithm

    • Topic | Exponential Laws
    • Example
      • Function : e^x + e^(2*x) + e^y + e^(2*y) = 12. Express as y = F(x)
      • Function : e^x + e^(2*x) + e^y + e^(2*y) = 12. Sketch the curve

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    AL 07. Binomial Theorem

    • Topic | Binomial Theorem : Expansion coefficients and sequences
    • Example : Binomial expansion coeff properties
      • Prove that Sum[C(n,r)] = 2^n for r=0,1,2,3,....n
      • Prove that Sum[C(n,r)] = C(n,n-r)
    • Example : Series in Pascal triangle
      • Prove that Sum[n*(n+1)/2] = n*(n+1)*(n+2)/3!
      • Prove that Sum[C(n+1,2)] = C(n+2,3)

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    AL 08. Series

    • Topic | Sequence and series
    • Outlines
      • Arithmetic series and examples
      • Geometric series and examples
      • Sequence ans series in Pascal triangle
      • Special series
    • Formula
      • Sum[n^1] = n*(n+1)/2
      • Sum[n^2] = n*(n+1)*(2*n+1)/6
      • Sum[n^3] = (n*(n+1)/2)^2
      • Sum[C(n+1,2)] = C(n+2,3)
      • Sum[C(n+2,3)] = C(n+3,4)
      • Sum[C(n+3,4)] = C(n+5,6)

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    AL 09. Logarithm
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    AL 10. Partial Fraction

    • Topic | Partial Fractions
    • Example 1 : Find partial fraction of y = 1/(x^3 + 1)
    • Example 2 : Find partial fraction of y = 1/(x^3 - 1)

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    AL 11. Equations

    • Topic | Equations
    • Solve quadratic equation
    • Solve cubic equation

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    AL 12. Complex Numbers

    • Topic | Complex Numbers
    • Example
      • What is DeMoivre's theorem ?
      • If z^5 = (1 + i), find z.

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    AL 13. Matrix and properties
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    AL 14. Mathematical Induction

    • Topic | Mathematcal Induction
    • Examples : Use induction method prove that
      • 1. Sum[n*(n+1)/2] = n*(n+1)*(n+2)/6
      • 2. Sum[n^2] = n*(n+1)*(2*n+1)/6
      • 3. Sum[n^3] = (n*(n+1)/2)^2
    • Reference : See keyword series in Webpage MD

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    AL 15. Inequalities
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    AL 16. Rational function


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    AL 17. Probabiliy
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    AL 18. DeMoivre's Theory

    • Topic | DeMovire's theory
    • Example 1 : Solve x^5 - 1 = 0 by construction
    • Example 2 : Solve x^4 + x^3 + x^2 + x + 1 = 0 by construction

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    AL 19. Indefinite equations
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    AL 20. Algebra Index

    • Topic | Algebra Index
    • How to find keyword ?
      • Find the section number and topic number of keyword
      • 1st number : Section number
      • 2nd number : Topic number
      • Remeber these two numbers
      • Click Back to back subject page
      • Click "Goto Begin" to top
      • Click section number to enter the required section
      • Click topic number

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    AL 21. Graphs of y = F(x)

    • Topic | Graphs of y = F(x)
    • Contents : There are 43 functions. First 5 are given as below
      • 1. y = a*x + b
      • 2. y = a*x^2 + b*x + c
      • 3. y = a*x^3 + b*x^2 + c*x + d
      • 4. y = a*x^4 + b*x^3 + c*x^2 + d*x + e
      • 5. y = a*x^5 + b*x^4 + c*x^3 + d*x^2 + e*x + f
    • Application examples
      • Graph y = (x-5)*(x-7)*(x+4)*(x+6) - 504. Find zeros of y
      • Solve (x-5)*(x-7)*(x+4)*(x+6) = 504.

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    AL 22. Glossary
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    AL 23. Home Work

    • Topic | Math Home works
    • Questions in algebra, geometry and trigonometry

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    AL 24. References

    • Topic | References
    • Topics
      • Mathematics on Internet
      • Mathematics on PC computer

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    AL 25. Examples : Questions in alphabetic order

    • Topic | Examples : Questions in alphabetic order
    • Methods
      • 1. Find the question
      • 2. Write down the question number (or remeber it)
      • 3. Goto top and Open MD with AL,AN, ....
      • 4. Click Topic AL
      • 5. Click AL to enter Algebra
      • 6. Use 1st number in question number to find subject
      • 7. Use 2nd number in question number to find the requred topic
      • 8. Example : Question number is 03 02
        • Subject : Number
        • Topic : ?

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    AL 26. Algebra Formulae
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    AL 27. Examples with solutions

    • Topic | Examples with solutions
    • Method
      • Find example from the list
      • Click that example to find solution

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    AL 00. Tips

    Index and examples
    • Lesson 20 : Index
    • Lesson 21 : Application graphic programs
    • Lesson 22 : Glossary
    • Lesson 23 : Goto home works
    • Lesson 24 : References
    • Lesson 25 : Examples link to section numbers, e.g. 03 02
    • Lesson 26 : Formulae in calculus
    • Lesson 27 : Select examples with solution (QA)
    Highlight tops (Update later)
    • 1. Series in section 8
    • 2. Sum[n*(n+1)/2!] = n*(n+1)*(n+2)/3! in 07 04
    • 3. Sum[n^2] = n*(n+1)*(2*n+1)/3! in 08 03
    Run Application graphic program (See Lesson 21)
    • Step 1 : Run at current location (no download)
    • Step 2 : Select Yes to run
    • Notes
      • 1. The application program is only for internet use (Update monthly)
      • 2. Download only available upto end of the month

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    Show Room of MD2002 Contact Dr. Shih Math Examples Room
    Copyright © Dr. K. G. Shih. Nova Scotia, Canada.
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