Math 149. Capstone Mathematics for Teachers. Spring 2011.
Tentative class schedule with homework assignments
This schedule is subject to change.
| Feb 1: | Last day to ADD classes without special permission. Last day to DROP classes without instructor's permission. | ||
| Feb 15: | Last day to DROP classes without a serious and compelling reason. | ||
| Apr 19: | Last day to WITHDRAW from a course for a serious and compelling reason | ||
| Date | Reading assignment | Written homework due | Topic & class activities |
| Jan 21 | - | - | Introduction. Syllabus & Schedule. Field Experience. Single Subject Credential Requirements. Who this class is for (and why to take it), etc. An advanced perspective. Natural numbers, Integers. Operations, properties. Divisibility. Decimal (base 10) representation, applications. Bases other than 10. Problems, Solutions |
| Jan 28 | Bases other than 10 (for Hoover High math club) | Homework 1 (Integers: divisibility and bases) | Field experience update: MFD and prep sessions Homework 1 discussion. Hoover High problems (bases other than 10) cont. Counting (combinatorics). Hoover High Problems, Solutions, MFD Prep problems, Solutions |
| Feb 4 | - | Homework 2 (Combinatorics) | Homework 2 discussion. Binomial Theorem, Probability. MFD Prep problems (cont.), Solutions |
| Feb 11 | - | Homework 3 (Binomial theorem, probability, rates) | Homework 3 discussion. Ratios, rates, proportional reasoning. Problems to work on in class, Hoover High problems |
| Feb 18 | - | Homework 4 (Ratios, rates, proportional reasoning) | Homework 4 discussion. Proportional reasoning in geometry (similarity). Areas and volumes of similar figures/solids. Problems on similarity Review: Study Guide and Sample Problems |
| Feb 25 | - | - | Test 1 (bases, divisibility, combinatorics, binomial theorem, probability, ratios, proportional reasoning, similarity). Test discussion. Experiment with an "arithmetic class". Natural numbers revisited. Axiomatic construction of natural numbers (Peano postulates for N; well-ordering principle; mathematical induction. |
| Mar 4 | Construction of the Number Systems: pages 1-3, pages 4-5 (Beachy and Blair, Abstract Algebra, 3rd ed., A2-A3) | - | Presentation: problem-solving (MFD prep) session. Integers revisited. Construction: integers as equivalence classes of pairs (differences) of natural numbers; properties of integers. Rational numbers. Construction: rational numbers as equivalence classes of pairs (quotients) of integers. |
| Mar 11 | Homework 5 (Rational and irrational numbers) | Homework 5 discussion. Field Experience: schedule update Rational numbers (cont.) Definition used in high school. Rational numbers as terminating/repeating decimals. Real numbers. Construction: real numbers as equivalence classes of Cauchy sequences of rational numbers. Complex numbers. Definition. |
|
| Mar 18 | Homework 6 (Complex numbers) | Homework 6 discussion.
Complex numbers (cont.) Rectangular and polar representations and their advantages. Algebraic structure of number sets. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields |
|
| Mar 25 | - | Homework 7 (Real fields) | Homework 7 discussion.
Functions. Definitions of important terms (graph, intercepts, roots, domain, codomain, range, asymptotes). Review: Study Guide and Sample Problems |
| Apr 1 | - | Homework 8 (Polynomials) | Homework 8 discussion. Test 2 (Number sets, functions). Test discussion. Important classes of functions. Polynomials. Definition. Operations with polynomials. Comparing the algebraic structure of polynomials with that of numbers. Graphs of polynomials. Solving polynomial inequalities. |
| Apr 8 | - | Homework 9 (Polynomial inequalities) | Homework 9 discussion.
Quadratic Polynomials. More on graphs of quadratic polynomials and solving quadratic inequalities. Equations. The concept of equation. Quadratic formula. Factoring quadratic polynomials. More on graphs of quadratic polynomials. Solving polynomial equations. Discussion of classroom observations and extracurricular activities. |
| Apr 15 | Homework 10 (Using calculators) | Homework 10 discussion. Geometry. Proofs of the Pythagorean theorem. Distance formula, equations of circle and ellipse. Coordinate geometry problems - do at least first 2 pages |
|
| Apr 22 | Spring recess - no classes, no office hours | ||
| Apr 29 | Homework 11 (Approximating the number pi) | Homework 11 discussion. Presentations: Field Experience |
|
| May 6 | Homework 12 (Technology) | Presentations: Field Experience (continued). Technology. Using technology, such as Geometer's sketchpad, Mathematica, Maple, etc. for creating exams and handouts. Final Exam (take-home) |
|
| May 12 | Faculty consultation day. Consultation hours: TBA. | ||
| May 13 | Faculty consultation day. Consultation hours: TBA. | ||
| May 18 | - | - | Final Exam due: submit via email (typed) by 11:59 PM. |