Math 149. Capstone Mathematics for Teachers. Spring 2016.
Tentative class schedule with homework assignments
This schedule is subject to change.
| Feb 1: | Last day to ADD classes without instructor's permission. | ||
| Feb 16: | 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 20 | - | - | Introduction. Syllabus & Schedule. Field Experience. Single Subject Credential Requirements. Who this class is for (and why to take it), etc. An advanced perspective. Overview of the field experience. Math Field Day and prep sessions. |
| Jan 25 | Natural numbers, Integers.
Divisibility. Divisibility tests for 2, 3, 9. Decimal (base 10) representation, applications. Bases other than 10: definition and examples. |
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| Jan 27 | Bases other than 10 | Bases other than 10 continued. High school math club problems, Solutions | |
| Feb 1 | - | Homework 1 | Homework 1 discussion. Choose problems for the February 18 MC/PSP. |
| Feb 3 | - |
Divisibility tests for bases other than 10. Counting (combinatorics). MFD Prep problems, Solutions |
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| Feb 4 | 5:00-7:00 PM, S2 145. Problem solving playground with high school students. | ||
| Feb 8 | - | Homework 2 | Homework 2 discussion. Binomial Theorem. Probability. High school math club problems, Solutions |
| Feb 10 | - | - | Ratios, rates, proportional reasoning. High school math club problems |
| Feb 15 | President's day - campus closed | ||
| Feb 17 | - | Homework 3 | Homework 3 discussion. Preparation for field experience. Proportional reasoning in geometry (similarity). Areas and volumes of similar figures/solids. Problems on similarity |
| Feb 18 | 5:00-7:00 PM, S2 145. Problem solving playground with high school students. | ||
| Feb 22 | - | Homework 4 | Homework 4 discussion. |
| Feb 24 | - | - | Review: Study Guide and Sample Problems |
| Feb 29 | - | - | Test 1 (divisibility, bases, combinatorics, binomial theorem, probability, ratios, proportional reasoning, similarity). Test discussion. |
| Mar 2 | Construction of the Number Systems: pages 1-3, pages 4-5 (Beachy and Blair, Abstract Algebra, 3rd ed., A2-A3) | - | Preparation for field experience. 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. |
| Mar 3 | 5:00-7:00 PM, S2 145. Problem solving playground with high school students. | ||
| Mar 7 | - | - | Rational numbers.
Definition used in high school. Formal construction of rational numbers (as equivalence classes of pairs of integers).
Rational numbers as terminating/repeating decimals.
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| Mar 9 | - | Homework 5 | Homework 5 discussion. Real numbers. Construction of real numbers as equivalence classes of Cauchy sequences of rational numbers. Complex numbers. Definition and representation in R2 using rectangular and polar coordinates. Geometric interpretation of complex numbers multiplication. |
| Mar 14 | - | - | Discussion of field experience. Algebraic structure of number sets. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields |
| Mar 16 | - | Homework 6 | Homework 6 discussion. More examples of groups and fields. |
| Mar 17 | 5:30-7:30 PM, S2 109. Math Kangaroo competition for grades 1-12. | ||
| 5:00-7:00 PM, S2 145. Problem solving playground with high school students. | |||
| Mar 21 | Spring recess | ||
| Mar 23 | Spring recess | ||
| Mar 28 | - | Homework 7 | Homework 7 discussion. More examples of groups and fields continued. Functions. Definitions of important terms (graph, intercepts, roots, domain, codomain, range, asymptotes). |
| Mar 30 | - | - | Functions continued. Questions Polynomials. Definition. Operations with polynomials. Comparing the algebraic structure of polynomials with that of numbers. |
| Apr 4 | - | Homework 8 | Homework 8 discussion. Equations. The concept of equation. Polynomial equations. Polynomials (cont.) Roots and graphs of polynomials. Solving polynomial equations and inequalities. |
| Apr 6 | - | - | Quadratic Polynomials. More on graphs of quadratic polynomials and solving quadratic equations and inequalities. Quadratic formula. Factoring quadratic polynomials. |
| Apr 7 | 6:40PM-??PM (rough estimate: until 9:30PM), S2 109. High School Integration Bee. Some help may be needed (contact Dr. Kay Kelm), observers welcome. To observe, no need to sign up in advance, just show up. |
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| Apr 11 | - | Homework 9 | Homework 9 discussion. Review: Study Guide and Sample Problems |
| Apr 13 | - | - | Test 2 (take home. Number sets, functions). |
| Apr 14 | 5:00-7:00 PM, S2 145. Problem solving playground with high school students. | ||
| Apr 16 | 8AM-4PM, on campus. Math Field Day competition for grades 6-12. As many helpers as possible are needed! Please sign up in advance. More information here. |
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| Apr 18 | - | - | Discussion of field experience. |
| Apr 20 | - | - | Geometry. Proofs of the Pythagorean theorem. Distance formula, equations of circle and ellipse. |
| Apr 25 | - | Homework 10 | Homework 10 discussion. Coordinate geometry problems |
| Apr 27 | - | - | Meet in S2 321 Technology. GeoGebra/Geometer's sketchpad |
| Apr 28 | 5:00-7:00 PM, S2 145. Problem solving playground with high school students. | ||
| May 2 | - | Homework 11 | Meet in S2 321 Homework 11 discussion. LaTeX: Sample LaTeX file, required image file Install LaTeX: MiKTeX (PC), TeXShop (Mac) On-line LaTeX manual, On-line collaborative LaTeX compilator |
| May 4 | - | - | Meet in S2 321 Mathematica/Maple |
| May 9 | - | Homework 12 | Meet in S2 321 Homework 12 discussion. Technology (cont.) |
| May 11 | - | - | Presentations: Field Experience Final Project |
| May 12 | Faculty consultation day. Consultation hours: 8:30-12:30, in PB 340 | ||
| May 18 | - | - | Final Project due: submit via email (typed) by 11:59 PM. |