Category Archives: Algebra

College algebra course at LSCS

College Algebra – Review of Basic Concepts

  1. Sets
    1. Basic Definition: sets written using {}, element of set E, not element of a set E, name sets with capital letters (ex. S), infinite set=unending list of distinct elements, finite set=limited number of elements, natural (counting) numbers, ellipsis points (…) the list of elements of the set continues according to the established pattern, a variable (ex. x) an arbitrary element of the set (set builder notation)
    2. Operations on Sets: Let A and B be sets, with unversal set U.
      1. complement: A’ = {x|x E U, x E A}
      2. intersection: A ^ B = {x|x E A and x E B}
      3. union: A U B = {x|x E A or x E B}
  2. Real Numbers and their properties: A number set with only positives is Natural, add Zero (0) and it becomes set Whole, add negative natural numbers, it gives Integers.  Divide 2 non-zero integers to get a rational number.  Real numbers are on the number line.  Irrational numbers cannot be represented as quotients of integers.
    1. Set of Numbers and the Number Line
    2. Exponents
    3. Order of Operations
    4. Properties of Real Numbers
    5. Order on the Number Line
    6. Absolute Value
  3. Polynomials
  4. Factoring Polynomials
  5. Rational Expressions
  6. Rational Exponents
  7. Radical Expressions