Course Topics
• Sets: explanation, representation/notation, elements/subsets, unions, intersections, a few rules, Cartesian product.
• Functions: general definitions, examples, real functions as important special case.
• Very brief re-introduction of natural numbers, integers, rational and real numbers with basic arithmetic rules, percentages. Manipulating algebraic expressions, factoring out and expanding, manipulating fractions, polynomials.
• Absolute values, powers and roots, exponentials, logarithms: definition, computation, rules.
• Real functions: tables of values and graphical representation, absolute value function, polynomial (linear, higher degrees) and power functions, exponential and logarithmic functions.
• Solving linear equations with one variable, a complete case study of quadratic equations including graphs, equations which can be solved via taking logarithms.
• Solving two linear equations with two variables simultaneously, cases with none, one and infinitely many solutions, graphical interpretation as intersection of lines.
• Solving inequalities (optional): linear inequalities in one and two variables, inequalities involving absolute values in one variable.
• Definition of factorials and permutations, binomial coefficients, Pascal's triangle and combinations.
Propaedeutic courses
none
Teaching format
lectures