Math 149. Capstone Mathematics for Teachers. Spring 2012.
Tentative class schedule with homework assignments
This schedule is subject to change.
| Jan 30: | Last day to ADD classes without special permission. | ||
| Feb 13: | Last day to DROP classes without a serious and compelling reason. | ||
| Apr 17: | Last day to WITHDRAW from a course for a serious and compelling reason | ||
| Date | Reading assignment | Written homework due | Topic & class activities |
| Jan 17 | - | - | 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 24 | Bases other than 10 (for Hoover High math club) | Homework 1 (Integers: divisibility and bases) | Homework 1 discussion. Hoover High problems (bases other than 10) cont. Counting (combinatorics). Hoover High Problems, Solutions |
| Jan 31 | - | Homework 2 (Combinatorics) | Homework 2 discussion. Binomial Theorem, Probability. MFD Prep problems, Solutions |
| Feb 7 | - | Homework 3 (Binomial theorem, probability, rates) | Homework 3 discussion. Ratios, rates, proportional reasoning. Problems to work on in class, Hoover High problems |
| Feb 14 | - | 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 21 | - | Homework 5 (Similarity and measurements) | Test 1 (bases, divisibility, combinatorics, binomial theorem, probability, ratios, proportional reasoning, similarity). Test discussion. Homework 5 discussion. |
| Feb 28 | Construction of the Number Systems: pages 1-3, pages 4-5 (Beachy and Blair, Abstract Algebra, 3rd ed., A2-A3) | - | Natural numbers revisited. Axiomatic construction of natural numbers (Peano postulates for N; well-ordering principle;
mathematical induction.
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. Real numbers. Construction: real numbers as equivalence classes of Cauchy sequences of rational numbers. |
| Mar 6 | Homework 6 (Rational and irrational numbers) | Rational numbers (cont.) Definition used in high school.
Homework 6 discussion. Rational numbers as terminating/repeating decimals. Complex numbers. Definition. |
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| Mar 13 | Homework 7 (Complex numbers) | Homework 7 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 |
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| Mar 20 | - | Homework 8 (Real fields) | Homework 8 discussion.
Group quiz. Review: Study Guide and Sample Problems |
| Mar 27 | - | Homework 9 (Polynomials) | Test 2 (Number sets, functions). Homework 9 discussion. Polynomials. Definition. Operations with polynomials. Comparing the algebraic structure of polynomials with that of numbers. Functions. Definitions of important terms (graph, intercepts, roots, domain, codomain, range, asymptotes). |
| Apr 3 | Spring recess - no classes, no office hours | ||
| Apr 10 | - | Homework 10 (Polynomial inequalities) | Equations. The concept of equation. Polynomial equations. Polynomials (cont.) Roots and graphs of polynomials. Solving polynomial equations and inequalities. Homework 10 discussion. Quadratic Polynomials. More on graphs of quadratic polynomials and solving quadratic equations and inequalities. Quadratic formula. Factoring quadratic polynomials. Preparation for the upcoming Hoover High Math League meeting (Coordinate Geometry). |
| Apr 17 | Homework 11 (Using calculators) | Homework 11 discussion. Geometry. Proofs of the Pythagorean theorem. Distance formula, equations of circle and ellipse. Coordinate geometry problems - do at least first 2 pages |
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| Apr 24 | Homework 12 (Approximating the number pi) | Homework 12 discussion. Technology. Using technology, such as LaTeX, GeoGebra/Geometer's sketchpad, Mathematica/Maple, etc. for creating exams and handouts. |
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| May 1 | Homework 13 (Technology) | Presentations: Field Experience Technology (cont.) More on LaTeX: On-line LaTeX manual, On-line LaTeX file compilator |
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| May 8 | Presentations: Field Experience (cont.) Technology (cont.) Sample LaTeX file, required image file Final Exam (take-home) |
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| May 10 | Faculty consultation day. Consultation hours: 12 - 2 PM. | ||
| May 11 | Faculty consultation day. Consultation hours: 10 AM - 12 PM. | ||
| May 17 | - | - | Final Exam due: submit via email (typed) by 11:59 PM. |