Math 149. Capstone Mathematics for Teachers. Spring 2015.
Tentative class schedule with homework assignments
This schedule is subject to change.
| Jan 29: | Last day to ADD classes without instructor's permission. | ||
| Feb 12: | Last day to DROP classes without a serious and compelling reason. | ||
| Apr 14: | Last day to WITHDRAW from a course for a serious and compelling reason | ||
| Date | Reading assignment | Written homework due | Topic & class activities |
| Jan 15 | - | - | 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 20 | Finalize dates/times of problem solving sessions. Natural numbers, Integers. Operations, properties. Divisibility. Divisibility tests for 2, 3, 9. Decimal (base 10) representation, applications. |
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| Jan 22 | Bases other than 10 | Bases other than 10. High school math club problems, Solutions | |
| Jan 27 | - | Homework 1 | Homework 1 discussion. Divisibility tests for bases other than 10. Choose topics for the problem solving sessions. |
| Jan 29 | - |
Counting (combinatorics), Binomial Theorem. MFD Prep problems, Solutions High school math club problems, Solutions |
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| Feb 3 | - | Homework 2 | Homework 2 discussion. (Brief discussion/review of a few topics that came up in the homework problems). |
| Feb 5 | - | - | Areas and volumes of important figures and solids. Perimeter as the derivative of area and surface area as the derivative of volume. |
| Feb 10 | - | Homework 3 | Homework 3 discussion. Ratios, rates, proportional reasoning. High school math club problems |
| Feb 12 | - | - | Proportional reasoning in geometry (similarity). Areas and volumes of similar figures/solids. Problems on similarity |
| Feb 17 | - | Homework 4 | Homework 4 discussion. Review: Study Guide and Sample Problems |
| Feb 19 | - | - | Test 1 (divisibility, bases, combinatorics, binomial theorem, probability, ratios, proportional reasoning, similarity). Test discussion. |
| Feb 24 | - | - | Preparation for field experience: Problems for the first problem solving session, 2/27, on composition of functions and complex numbers. Complex numbers. Definition and representation in R2 using rectangular and polar representations. Geometric interpretation of complex numbers multiplication. |
| Feb 26 | 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. |
| Feb 27 | - | 4-6PM, room ED 390. Problem solving session for grades 6-12. Topics: composition of functions, complex numbers. Problems with solutions |
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| Mar 3 | - | Homework 5 | Homework 5 questions/answers. Rational numbers. Construction of rational numbers as equivalence classes of pairs of integers and the definition used in high school. Real numbers. Construction: real numbers as equivalence classes of Cauchy sequences of rational numbers. |
| Mar 5 | - | - | Rational numbers (cont.) Rational numbers as terminating/repeating decimals. Preparation for field experience: Problems for the second problem solving session, 3/7, on number theory. |
| Mar 7 | - | 1-3PM, room PB 011. Problem solving session for grades 9-12. Topic: number theory. Problems with solutions |
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| Mar 10 | - | Homework 6 | Homework 6 discussion. Preparation for field experience: Problems for the third problem solving session, 3/14, on the number pi, area, volume |
| Mar 12 | - | - | Preparation for field experience cont. Algebraic structure of number sets. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields |
| Mar 14 | - | 9-11AM, room S2 109. Problem solving session for grades 9-12. Topics: the number pi, area, volume. Problems - pdf |
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| Mar 17 | - | Homework 7 | Homework 7 discussion.
Functions. Definitions of important terms (graph, intercepts, roots, domain, codomain, range, asymptotes). Questions |
| Mar 19 | - | - | Polynomials. Definition. Operations with polynomials. Comparing the algebraic structure of polynomials with that of numbers. Preparation for field experience: Math Kangaroo problems |
| 5:45-8PM, UBC 192. Math Kangaroo competition for grades 1-12. Helpers: Ricardo, Nick, Carlie. More helpers welcome! | |||
| Mar 24 | - | Homework 8 | Homework 8 discussion. Discussion of off campus field experience. Review: Study Guide and Sample Problems |
| Mar 26 | - | - | Test 2 (Number sets, functions). Test discussion. |
| Mar 31 | Spring recess | ||
| Apr 2 | Spring recess | ||
| Apr 7 | - | Homework 9 | Homework 9 discussion. Equations. The concept of equation. Polynomial equations. Polynomials (cont.) Roots and graphs of polynomials. Solving polynomial equations and inequalities. |
| Apr 8 | - | - | 6:40PM-??PM (rough estimate: until 9:30PM), S2 109. High School Integration Bee. Some help needed, observers welcome. No need to sign up in advance, just show up. |
| Apr 9 | - | - | Quadratic Polynomials. More on graphs of quadratic polynomials and solving quadratic equations and inequalities. Quadratic formula. Factoring quadratic polynomials. |
| Apr 14 | - | Homework 10 | Homework 10 discussion. Geometry. Proofs of the Pythagorean theorem. |
| Apr 16 | - | - | Distance formula, equations of circle and ellipse. Coordinate geometry problems |
| Apr 18 | - | - | 7AM-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. |
| Apr 21 | - | Homework 11 | Meet in S2 321 Homework 11 discussion. Technology. GeoGebra/Geometer's sketchpad |
| Apr 23 | - | - | Meet in S2 321 Mathematica/Maple |
| Apr 28 | - | Homework 12 | Meet in S2 321 Homework 12 discussion. LaTeX: Sample LaTeX file, required image file Install LaTeX: MiKTeX (PC), TeXShop (Mac) On-line LaTeX manual, On-line LaTeX file compilator |
| Apr 30 | - | - | Presentations: Field Experience |
| May 5 | - | - | Presentations: Field Experience (cont.) Technology (cont.) Final Project |
| May 7 | Faculty consultation day. Consultation hours: 8:00-9:30 AM | ||
| May 8 | Faculty consultation day. Consultation hours: 8:30-11:00 AM | ||
| May 14 | - | - | Final Project due: submit via email (typed) by 11:59 PM. |