Math 149. Capstone Mathematics for Teachers. Spring 2017.
Tentative class schedule with homework assignments
This schedule is subject to change.
| Jan 30: | Last day to ADD classes without instructor's permission. | ||
| Feb 6: | Last day to DROP classes online. | ||
| Feb 13: | Last day to DROP classes with a paper form without a serious and compelling reason. | ||
| May 10: | 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. An advanced perspective. Overview of the field experience. Math Circle, Math Field Day, Math Kangaroo, prep sessions. |
| Jan 19 | Natural numbers, Integers.
Divisibility. Divisibility tests for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 25, 100. Decimal (base 10) representation. |
||
| Jan 21 | 9:45-11:30 AM. Math Circle, grades 3-10. | ||
| Jan 24 | Bases other than 10 | Bases other than 10, definition, examples, applications, problems. Math club problems, Solutions | |
| Jan 26 | - | Other bases cont. Divisibility tests in other bases. |
|
| Jan 28 | 9:45-11:45 AM, 1:30-3:30 PM. Math Kangaroo Prep (grades 1-6 in the morning, 7-12 in the afternoon). | ||
| Jan 31 | - | Homework 1 |
Homework 1 discussion. Choose problems for the February 11 Math Field Day prep, grades 9-10. Counting (combinatorics). MFD Prep problems, Solutions |
| Feb 2 | - | Homework 2 | Homework 2 discussion. Combinatorics cont. Math club problems, Solutions |
| Feb 4 | 9:45-11:30 AM. Math Circle, grades 3-10. | ||
| Feb 7 | - | - | Combinatorics cont. Binomial Theorem. Probability. |
| Feb 9 | - | Homework 3 | Homework 3 discussion.
Ratios, rates, proportional reasoning. Math club problems |
| 5:30PM-7:30PM. Math Circle, grades 10-12. | |||
| Feb 11 | 9:00AM-12:00PM. Math Field Prep (grades 7-12). | ||
| Feb 14 | - | - | Proportional reasoning in geometry (similarity).
Areas and volumes of similar figures/solids. Problems on similarity Discussion of and preparation for field experience. |
| Feb 16 | - | Homework 4 | Homework 4 discussion. Review: Study Guide and Sample Problems |
| Feb 18 | 9:45-11:30 AM. Math Circle, grades 3-10. | ||
| Feb 21 | - | - |
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. |
| Feb 23 | Construction of the Number Systems: pages 1-3, pages 4-5 (Beachy and Blair, Abstract Algebra, 3rd ed., A2-A3) | - | 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. |
| 5:30PM-7:30PM. Math Circle, grades 10-12. | |||
| Feb 25 | 9:45-11:45 AM, 1:30-3:30 PM. Math Kangaroo Prep (grades 1-6 in the morning, 7-12 in the afternoon). | ||
| Feb 28 | - | - | Test 1 (divisibility, bases, combinatorics, binomial theorem, probability, ratios, proportional reasoning, similarity).
Test discussion. |
| Mar 2 | - | 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 4 | 9:45-11:30 AM. Math Circle, grades 3-10. | ||
| Mar 7 | - | - | Algebraic structure of number sets. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields. More examples of groups and fields, e.g. braid group. |
| Mar 9 | - | Homework 6 | Homework 6 discussion. More examples of groups and fields continued. Discussion of field experience. |
| 5:30PM-7:30PM. Math Circle, grades 10-12. | |||
| Mar 11 | 9:45-11:45 AM, 1:30-3:30 PM. Math Kangaroo Prep (grades 1-6 in the morning, 7-12 in the afternoon). | ||
| Mar 14 | - | - | Functions. Definitions of important terms (graph, intercepts, roots, domain, codomain, range, asymptotes). |
| Mar 16 | - | Homework 7 | Homework 7 discussion. Functions continued. |
| 5:30-7:30 PM, ED 140. Math Kangaroo competition for grades 1-12. | |||
| Mar 18 | 9:45-11:30 AM. Math Circle, grades 3-10. | ||
| Mar 21 | - | - | Functions continued. Equations. The concept of equation. Questions. |
| Mar 23 | - | Homework 8 | Homework 8 discussion. Polynomials. Polynomial equations. Roots and graphs of polynomials. Solving polynomial equations and inequalities. |
| 5:30PM-7:30PM. Math Circle, grades 10-12. | |||
| Mar 25 | 9:45-11:45 AM. Math Kangaroo solutions, grades 1-12 (followed by the awards ceremony) | ||
| Mar 28 | - | Quadratic Polynomials. More on graphs of quadratic polynomials and solving quadratic equations and inequalities. Quadratic formula. Factoring quadratic polynomials. | |
| Mar 30 | - | Homework 9 | Homework 9 discussion. Review: Study Guide and Sample Problems |
| Apr 1 | 9:45-11:30 AM. Math Circle, grades 3-10. | ||
| Apr 4 | - | - | Test 2 (Number sets, functions). |
| Apr 5 | 6:45PM until winners have been determined (until 8:30-10PM in the past). High School Integration Bee. S2 109. | ||
| Apr 6 | - | Homework 10 | Homework 10 discussion. Discussion of field experience. |
| 5:30PM-7:30PM. Math Circle, grades 10-12. | |||
| Apr 8 | 9:00AM-12:00PM. Math Field Prep (grades 7-12). | ||
| Apr 11 | Spring recess | ||
| Apr 13 | Spring recess | ||
| Apr 15 | 9:45-11:30 AM. Math Circle, grades 3-10. | ||
| Apr 18 | - | - | Geometry. Proofs of the Pythagorean theorem. Distance formula, equations of circle and ellipse. |
| Apr 20 | - | - | Coordinate geometry problems |
| 5:30PM-7:30PM. Math Circle, grades 10-12. | |||
| Apr 22 | 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. |
||
| Apr 25 | - | - | Bring your laptops to class Technology. LaTeX: Sample LaTeX file, required image file Install LaTeX: MiKTeX (PC), TeXShop (Mac) On-line LaTeX manual, On-line collaborative LaTeX compilator (Overleaf) |
| Apr 27 | - | Homework 11 | Bring your laptops to class Homework 11 discussion. TikZ package: Sample file, Manual |
| Apr 29 | 9:45-11:30 AM. Math Circle, grades 3-10. | ||
| May 2 | - | - | Bring your laptops to class Intro to Mathematica, Wolfram sign-in page |
| May 4 | - | Homework 12 | Bring your laptops to class Homework 12 discussion. Presentations: Field Experience |
| 5:30PM-7:30PM. Math Circle, grades 10-12. | |||
| May 9 | - | - | Presentations: Field Experience (cont.) Final Project |
| May 11 | Faculty consultation day. Consultation hours: 9-12 and 1-3 in PB 340 | ||
| May 13 | 9:45-11:30 AM. Math Circle, grades 3-10. | ||
| May 18 | - | - | Final Project due: submit via email (typed in LaTeX) by 11:59 PM. |