Advanced Algebra

TABLE OF CONTENTS

• FOUNDATIONS -- What should be learned at school:
  • NUMBERS: whole numbers, decimals, fractions, percents, negative numbers, prime and composite numbers, exponents and roots, logarithms, irrational numbers, imaginary numbers, sets, etc;
  • POLYNOMIALS: terms, constant, variables, exponents, degrees, standard forms;
  • FUNCTIONS: domain, range, increasing or decreasing, maxima and/or minima, even or odd.
• SKILLS -- What is expected to make oneself master of:
  • Solving and graphing different forms of linear equations, quadratic equations, inequalities and systems of equations;
  • Factorization of polynomials and its applications;
  • Function transformation;
  • Operations with functions, composition of functions and inverse functions;
  • Arithmetic sequence and geometric sequence;
  • Probability - combinations and permutations.
• STRUCTURE -- What is missing in general education but is essential for advanced study in higher education institutions:
  • The relationship between equation/inequality and its graph;
  • Mathematical modeling and interpretation;
  • Identification of sub-topics from description of math problems;
  • Connection among different topics and how these inter-linkage helps us understand an unknown/complex problem.
• HABIT -- What is helpful to learn math well
  • Write neatly
  • Graph or Sketch
  • Seek multiple solutions / explanations
  • Communicate with ones brain instead of calculator