MA 110 Fall 2003                 

Algebra Lecture Notes


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  1. Logic and Sets
    1. Propositional Logic
    2. Sets
    3. Boolean Algebras
  2. Numbers
    1. Fields
    2. Induction and Order of Operations
    3. Unique Factorization
    4. Numerals and Geometric Series
    5. Ordered Fields
    6. Decimal Expansions
    7. Complex Numbers
    8. Solving Equations
    9. Number Line and Plane
    10. Functions
  3. Geometry
    1. The Pythagorean Theorem
    2. Trigonometry
    3. Polar Coordinates and Transformations
    4. Lines, Circles, and Parabolas
    5. Conic Sections
  4. Polynomials
    1. Polynomials
      1. Graphing Near a Point
    2. Rational Roots
    3. The Fundamental Theorem of Algebra
    4. Cubic Equations
    5. Quartic Equations
  5. Continuity and the Fundamental Theorem of Algebra
    1. Continuity
    2. More Continuous Functions
    3. Theorems of Bolzano and Weierstrass
    4. The Proof of the Fundamental Theorem of Algebra
  6. Elementary Functions
    1. Exponential Functions
    2. Inverse Functions
    3. Logarithmic Functions
    4. Power Series