Math 149S. Capstone Mathematics for Teachers. Spring 2021.
Tentative class schedule with homework assignments
This schedule is subject to change.
| Feb 3: | Last day to ADD classes without instructor's permission | ||
| Feb 18: | Last day to DROP classes without a serious and compelling reason and without a grade of W (withdrawal) listed on university transcript | ||
| Apr 14: | Last day to WITHDRAW from classes for a serious and compelling reason | ||
| May 5: | CHANGE to/from CR/NC grading | ||
| See registration calendar for other important dates | |||
| Date | Reading assignment | Written homework due | Topic & class activities |
| Jan 25 | - | - | Introduction. Syllabus and Schedule. Overview of service learning. Math Circle, AMC, Math Kangaroo, Math Field Day, prep sessions. Sign-up sheet. |
| Jan 27 | Service Learning and Students
What is Service Learning? A Student's Guide to Successful Service Learning |
- | More on service learning.
Technology. LaTeX: On-line collaborative LaTeX compilator (Overleaf), On-line LaTeX manual, Sample slides TikZ package: Sample file, Manual |
| Jan 30 | 9:50-11:30 AM. Math Circle, grades 3-8, observers welcome. | ||
| Feb 1 | - | - | TikZ package continued |
| Feb 3 | - | Homework 1 | Homework 1 discussion. 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. |
| 5:30PM-7:30PM. Math Circle - AMC 10/12 practice, mostly grades 8-12 - participants welcome. | |||
| Feb 6 | 9:45-11:45 AM, 1:45-3:45 PM. Math Kangaroo Prep Grades 1-2, 5-6, in the morning, grades 3-4 and 7-8 in the afternoon - leaders needed. Grades 11-12 in the afternoon - observers welcome. |
||
| Feb 8 | Bases other than 10 | - | Bases other than 10, definition, examples, applications, problems. Math club problems, Solutions |
| Feb 10 | - | Homework 2: Service Learning Plan, First Draft | Other bases cont. Fractions in other bases. Place value problems. |
| 5:30PM-7:30PM. AMC 10/12 competition - proctors needed. | |||
| Feb 13 | 9:50-11:30 AM. Math Circle, grades 3-8 - observers welcome. | ||
| Feb 15 | Presidents' Day - no classes | ||
| Feb 17 | - | Homework 3 | Homework 3 discussion. Counting (combinatorics). MFD Prep problems, Solutions, Math club problems, Solutions |
| Feb 20 | 9:45-11:45 AM, 1:45-3:45 PM. Math Kangaroo Prep Grades 1-2, 5-6, in the morning, grades 3-4 and 7-8 in the afternoon - leaders needed. Grades 9-10 in the morning - participants welcome. |
||
| Feb 22 | - | - | Combinatorics cont. Binomial coefficients (n choose k). Fresno Math Circle 7-8 problems, Fresno Math Circle 11-12 problems. |
| Feb 24 | - | Homework 4 | Homework 4 discussion.
Binomial Theorem. Review: Study Guide and Sample Problems, updated |
| Feb 27 | 9:50-11:30 AM. Math Circle, grades 3-8 - observers welcome. | ||
| Mar 1 | - | - | Test 1 (on topics from Divisibility to Binomial Theorem). |
| Mar 3 | - | Probability.
Fresno Math Circle 11-12 problems: discrete probability, continuous probability. |
|
| 5:30PM-7:30PM. Math Circle, grades 9-12 - participants welcome. | |||
| Mar 6 | 9:45-11:45 AM, 1:45-3:45 PM. Math Kangaroo Prep Grades 1-2, 5-6, in the morning, grades 3-4 and 7-8 in the afternoon - leaders needed. Grades 9-10 in the morning, 11-12 in the afternoon - participants welcome. |
||
| Mar 8 | 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)
Integers revisited. Construction: integers as equivalence classes of pairs (differences) of natural numbers. |
|
| Mar 10 | - | Homework 5 | Homework 5 discussion. 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. Real numbers. Construction of real numbers as equivalence classes of Cauchy sequences of rational numbers. |
| 5:00PM-6:30PM. Math Field Day Prep, grades 6-8 - leaders needed. | |||
| Mar 13 | 9:50-11:30 AM. Math Circle, grades 3-8 - observers welcome. | ||
| Mar 15 | - | - | Complex numbers. Definition and representation in R2 using rectangular and polar coordinates. Geometric interpretation of complex numbers multiplication. |
| Mar 17 | - | Homework 6 | Homework 6 discussion. Algebraic structure of number sets. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields. |
| 5:30PM-7:30PM. Math Circle, grades 9-12 - MFD prep - participants welcome. | |||
| Mar 22 | - | - | Review: Study Guide and Sample Problems, updated |
| Mar 24 | - | Homework 7 | Test 2 (on topics from Probability to Algebraic Structures). |
| Mar 25 | 5:30PM-7:30PM. Math Field Day Prep, grades 9-12 - leaders needed. | ||
| Mar 27 | 9:50-11:30 AM. Math Circle, grades 3-8 - observers welcome. | ||
| Mar 29 | Spring recess | ||
| Mar 31 | Spring recess | ||
| Apr 5 | - | - | Functions. Definitions of important terms (function, domain, codomain, range, graph, intercept, root). |
| Apr 7 | - | Homework 8: Service Learning Plan, Final Version | Equations. The concept of equation. Questions. |
| 5:00PM-6:30PM. Math Field Day Prep, grades 6-8 - leaders needed. | |||
| Apr 8 | 5:30PM-7:30PM. Math Field Day Prep, grades 9-12 - leaders needed. | ||
| Apr 10 | 9:50-11:30 AM. Math Circle, grades 3-8 - observers welcome. | ||
| Apr 12 | - | - | Polynomials. Polynomial equations. Roots and graphs of polynomials. Solving polynomial equations and inequalities.
Overleaf file with this discussion. |
| Apr 14 | - | Homework 9 | Homework 9 questions/answers. Quadratic Polynomials. More on graphs of quadratic polynomials and solving quadratic equations and inequalities. Overleaf file with this discussion. Quadratic formula. Factoring quadratic polynomials. Vieta's formulas. Math Circle materials. |
| Math Circle, grades 9-12 - participants welcome. | |||
| Apr 17 | Math Field Day, grades 6-12 - helpers needed. | ||
| Apr 19 | - | Geometry. Proofs of the Pythagorean theorem. Coordinate Geometry. Distance formula. Equations of circle and ellipse. Coordinate geometry problems. |
|
| Apr 21 | - | Homework 10 | Homework 10 discussion. Similarity. Areas and volumes of similar figures/solids.
Math club problems. More problems on similarity. |
| Apr 24 | 9:50-11:30 AM. Math Circle, grades 3-8 - observers welcome. | ||
| Apr 26 | - | - | Review: Study Guide and Sample Problems, updated
Math Field Day games. Final Project |
| Apr 28 | - | Homework 11 | Test 3 (on topics from Functions to Similarity). |
| Math Circle, grades 9-12 - participants welcome. | |||
| May 3 | - | - | Presentations: Service Learning |
| May 5 | - | - | Presentations: Service Learning (cont.) |
| May 6 | Faculty consultation day. Consultation hours: 10:00 am - 12:00 pm and 1:00 pm - 3:00 pm at the Friday office hours zoom link | ||
| May 7 | Faculty consultation day. Consultation hours: 10:00 am - 12:00 pm at the Friday office hours zoom link | ||
| May 12 | - | - | Final Project due 11:59 PM. |