Math 149S. Capstone Mathematics for Teachers. Spring 2023.
Tentative class schedule with homework assignments
This schedule is subject to change.
| Feb 1 | Last day to ADD classes without permission | ||
| Feb 14 | Last day to DROP classes without a serious and compelling reason and without a grade of W (withdrawal) listed on university transcript | ||
| Apr 19 | Last day to DROP classes for a serious and compelling reason | ||
| See registration calendar for other important dates | |||
| Date | Reading assignment | Written homework due | Topic & class activities |
| Jan 19 | - | - | Introduction. Syllabus and Schedule. Overview of service learning. Math Circle, AMC, Math Kangaroo, Math Field Day, practice sessions. Sign-up sheet. |
| Jan 24 | Service Learning and Students
What is Service Learning? A Student's Guide to Successful Service Learning SL preference form (optional) SL sign-up sheet |
- | More on service learning.
Technology. LaTeX: On-line collaborative LaTeX compilator (Overleaf), On-line LaTeX manual, Sample slides. TikZ package: Sample file, Manual. Practice: Group 1, Group 2, Group 3, Group 4, Group 5, Group 6, Group 7. |
| Jan 26 | - | Service Learning Plan (complete and sign) | TikZ package continued |
| Jan 28 | 9:50-11:30 AM, PB 011, 012, 013. Math Circle, grades 3-8 - observers welcome. | ||
| Jan 31 | - | - | 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. |
| 5:30-7:30 PM, S2 208. AMC 8 solutions, mostly grades 5-8 - observers welcome. | |||
| Feb 1 | 5:30-7:30 PM, PB 013. Math Circle, grades 9-12 - participants welcome. | ||
| Feb 2 | Bases other than 10 | Homework 1 | Homework 1 discussion. Bases other than 10, definition, examples, applications, problems. Math club problems, Solutions. |
| Feb 4 | 10:00 AM-12:00 PM grades 1-2, 5-6, and 9-10, 1:30-3:30 PM grades 3-4, 7-8, and 11-12. PB 011, 012, 013.
Math Kangaroo Prep Grades 3-4, 5-6, and 7-8 leaders needed; grades 1-2 one helper needed; grades 9-10 and 11-12 participants welcome. |
||
| Feb 7 | - | - | Other bases cont. Fractions in other bases. Place value problems. Discussion on Service Learning: math competitions and competition practices. |
| Feb 9 | - | Homework 2 | Homework 2 discussion. Counting (combinatorics). Fresno Math Circle 7-8 problems, MFD Prep problems, Solutions, Math club problems, Solutions. |
| Feb 11 | 9:50-11:30 AM, PB 011, 012, 013. Math Circle, grades 3-8 - observers welcome. | ||
| Feb 14 | - | - | Combinatorics cont. Binomial coefficients (n choose k). Binomial Theorem. Fresno Math Circle 11-12 problems. |
| Feb 15 | 5:30-7:30 PM, PB 013. Math Circle, grades 9-12 - participants welcome. | ||
| Feb 16 | - | Homework 3 | Homework 3 discussion.
Probability. Fresno Math Circle 11-12 problems: discrete probability, continuous probability. |
| Feb 18 | 10:00 AM-12:00 PM grades 1-2, 5-6, and 9-10, 1:30-3:30 PM grades 3-4, 7-8, and 11-12. PB 011, 012, 013.
Math Kangaroo Prep Grades 3-4, 5-6, and 7-8 leaders needed; grades 1-2 one helper needed; grades 9-10 and 11-12 participants welcome. |
||
| Feb 21 | - | - | 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. |
| Feb 23 | Homework 4 | Homework 4 discussion.
Review: Study Guide and Sample Problems |
|
| Feb 25 | 9:50-11:30 AM, PB 011, 012, 013. Math Circle, grades 3-8 - observers welcome. | ||
| Feb 28 | - | Test 1 (on topics from Divisibility to Probability). | |
| Mar 1 | 5:30-7:30 PM, PB 013. Math Circle, grades 9-12 - participants welcome. | ||
| Mar 2 | Construction of the Number Systems (Beachy and Blair, Abstract Algebra, 3rd ed., A2-A3) | Service Learning: progress report 1 | 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. |
| Mar 4 | 10:00 AM-12:00 PM grades 1-2, 5-6, and 9-10, 1:30-3:30 PM grades 3-4, 7-8, and 11-12. PB 011, 012, 013.
Math Kangaroo Prep Grades 3-4, 5-6, and 7-8 leaders needed; grades 1-2 one helper needed; grades 9-10 and 11-12 participants welcome. |
||
| Mar 7 | - | - | Real numbers. Construction of real numbers as equivalence classes of Cauchy sequences of rational numbers. |
| Mar 8 | 5:00-7:00PM, PB 013. Math Field Day practice, grades 6-8 - leaders needed. | ||
| Mar 9 | - | Homework 5 | Homework 5 discussion. Complex numbers. Definition and representation in R2 using rectangular and polar coordinates. Geometric interpretation of complex numbers multiplication. |
| 5:30-7:30 PM, PB 032. Math Field Day practice, grades 9-12 - leaders needed. | |||
| Mar 11 | 9:50-11:30 AM, PB 011, 012, 013. Math Circle, grades 3-8 - observers welcome. | ||
| Mar 14 | - | - | Functions.
Definitions of important terms (function, domain, codomain, range, graph, intercept, root).
Discussion on Service Learning: teaching diverse students. |
| Mar 15 | 5:30-7:30 PM, PB 013. Math Circle, grades 9-12 - participants welcome. | ||
| Mar 16 | - | Homework 6 | Homework 6 discussion.
Equations. The concept of equation. Questions. |
| 4:30-8:00 PM, IT 290, 294. Math Kangaroo Competition, grades 1-12 - helpers needed. | |||
| Mar 21 | - | - | Polynomials. Polynomial equations. Roots and graphs of polynomials. Solving polynomial equations and inequalities.
Overleaf file with this discussion. |
| Mar 23 | - | Homework 7 | Homework 7 discussion.
Review: Study Guide and Sample Problems |
| Mar 25 | 9:50-11:30 AM, PB 011, 012, 013. Math Circle, grades 4-8 - observers welcome. | ||
| Mar 27 | 5:30-7:30 PM, S2 308. Math Field Day practice, grades 9-12 - leaders needed. | ||
| Mar 28 | - | - | Test 2 (on topics from Natural Numbers to Equations). |
| Mar 29 | 5:30-7:30 PM, PB 013. Math Circle, grades 9-12 - participants welcome. | ||
| Mar 30 | - | Service Learning: progress report 2 | 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. Problems, Math Circle materials. |
| 6:00-8:00 PM, PB 032. Math Field Day practice, grades 6-8 - leaders needed. | |||
| Mar 31 | Cesar Chavez Day - no classes, no office hours | ||
| Apr 1 | 10:00 AM-12:00 PM, PB 011, 012, 013, 101, 102, 103. Math Kangaroo Solutions and Awards, grades 1-12 - leaders needed for grades 3-4, 5-6, 7-8. | ||
| Apr 4 | Spring break | ||
| Apr 6 | Spring break | ||
| Apr 11 | - | - | Algebraic structures. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields. |
| Apr 12 | 5:30-7:30 PM, PB 013. Math Circle, grades 9-12 - participants welcome. | ||
| Apr 13 | - | Homework 8 | Homework 8 questions/answers. Geometry. Proofs of the Pythagorean theorem. Coordinate Geometry. Distance formula. Equations of circle and ellipse. Coordinate geometry problems. |
| Apr 15 | approx. 8:00AM-4:30 PM, various locations on campus. Math Field Day, grades 6-12 - helpers needed. | ||
| Apr 18 | - | - | Similarity. Areas and volumes of similar figures/solids.
Math club problems. More problems on similarity. |
| Apr 20 | - | Homework 9 | Homework 9 discussion. Proportional reasoning.
Discussion on Service Learning: mathematics in everyday life. |
| Apr 22 | 9:50-11:30 AM, PB 011, 012, 013. Math Circle, grades 3-8 - observers welcome. | ||
| Apr 25 | - | - | Math Field Day games. Final Project |
| Apr 26 | 5:30-7:30 PM, PB 013. Math Circle, grades 9-12 - participants welcome. | ||
| Apr 27 | - | Homework 10 | Homework 10 discussion.
Review: Study Guide and Sample Problems |
| May 2 | - | - | Test 3 (on topics from Polynomials to Similarity). |
| May 4 | - | - | Presentations: Service Learning |
| May 6 | 9:00-11:00 AM and 3:00-6:00 PM, S2 308. AMS conference, Special Sessions on Math Circle Games that Teach Deep Mathematics. | ||
| May 9 | - | - | Presentations: Service Learning (cont.)
Discussion on Service Learning: how did our work benefit the students and the community? |
| May 10 | 5:30-7:30 PM, PB 013. Math Circle, grades 9-12 - participants welcome. | ||
| May 11 | Faculty consultation day. Consultation hours: 9:30-10:30 AM and 2-3:15 PM | ||
| May 12 | Faculty consultation day. Consultation hours: 11 AM-12 PM and 2-3 PM | ||
| May 18 | - | - | Final Project due 11:59 PM. |