Math 149S. Capstone Mathematics for Teachers. Spring 2024.
Tentative class schedule with homework assignments
This schedule is subject to change.
Jan 31  Last day to ADD classes without permission  
Feb 13  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 18      Introduction. Syllabus and Schedule. Overview of service learning. Math Circle, AMC, Math Kangaroo, Math Field Day, practice sessions. Signup sheet. 
5:007:00 PM, EE 188. AMC 8 competition, mostly grades 58  helper found.  
Jan 20  10:0011:30 AM, PB 011, 012, 013. Math Circle, grades 49  observers welcome.  
Jan 23  Service Learning and Students
What is Service Learning? A Student's Guide to Successful Service Learning Safety Guielines for Service SL preference form (optional) SL signup sheet 
  More on service learning.
Technology. LaTeX: Online collaborative LaTeX compilator (Overleaf), Online 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 24  6:008:00 PM, S2 308. Math Circle, grades 1012  participants welcome.  
Jan 25    Service Learning Plan (complete and sign)  TikZ package continued 
Jan 30      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. 
Feb 1  Bases other than 10  Homework 1  Homework 1 discussion. Bases other than 10, definition, examples, applications, problems. Math club problems, Solutions. 
5:307:30 PM, EE 188. AMC 8 solutions, mostly grades 58  observers welcome.  
Feb 3  10:0011:30 AM, PB 011, 012, 013. Math Circle, grades 47  helpers needed, grades 89  observers welcome.  
Feb 6      Other bases cont. Fractions in other bases. Place value problems. Discussion on Service Learning: math competitions and competition practices. 
Feb 7  6:008:00 PM, S2 308. Math Circle, grades 1012  participants welcome.  
Feb 8    Homework 2  Homework 2 discussion. Counting (combinatorics). Fresno Math Circle 78 problems, MFD Prep problems, Solutions, Math club problems, Solutions. 
Feb 10  10:00 AM12:00 PM grades 12, 56, and 910, 1:303:30 PM grades 34, 78, and 1112. PB 011, 012, 013.
Math Kangaroo Practice Grades 34, 56, and 78 leaders needed; grades 12 one helper needed; grades 910 and 1112 participants welcome. 

Feb 13      Combinatorics cont. Binomial coefficients (n choose k). Binomial Theorem. Fresno Math Circle 1112 problems. 
Feb 15    Homework 3  Homework 3 discussion.
Probability. Fresno Math Circle 1112 problems: discrete probability, continuous probability. 
Feb 17  10:0011:30 AM, PB 011, 012, 013. Math Circle, grades 47  helpers needed, grades 89  observers welcome.  
Feb 20      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 21  6:008:00 PM, S2 308. Math Circle, grades 1012  participants welcome.  
Feb 22  Homework 4  Homework 4 discussion.
Review: Study Guide and Sample Problems 

Feb 24  10:00 AM12:00 PM grades 12, 56, and 910, 1:303:30 PM grades 34, 78, and 1112. PB 011, 012, 013.
Math Kangaroo Practice Grades 34, 56, and 78 leaders needed; grades 12 one helper needed; grades 910 and 1112 participants welcome. 

Feb 27    Test 1 (on topics from Divisibility to Probability).  
Feb 29  Construction of the Number Systems (Beachy and Blair, Abstract Algebra, 3rd ed., A2A3)  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 2  10:0011:30 AM, PB 011, 012, 013. Math Circle, grades 49  observers welcome.  
Mar 5      Real numbers. Construction of real numbers as equivalence classes of Cauchy sequences of rational numbers. 
Mar 6  6:008:00 PM, S2 308. Math Circle, grades 1012  participants welcome.  
Mar 7    Homework 5  Homework 5 discussion. Complex numbers. Definition and representation in R^{2} using rectangular and polar coordinates. Geometric interpretation of complex numbers multiplication. 
5:307:30PM, S2 206 (grades 68), S2 109 (grades 912). Math Field Day practice, grades 68  leaders needed, grades 912  participants welcome.  
Mar 9  10:00 AM12:00 PM grades 12, 56, and 910, 1:303:30 PM grades 34, 78, and 1112. PB 011, 012, 013.
Math Kangaroo Practice Grades 34, 56, and 78 leaders needed; grades 12 one helper needed; grades 910 and 1112 participants welcome. 

Mar 12      Functions.
Definitions of important terms (function, domain, codomain, range, graph, intercept, root).
Discussion on Service Learning: teaching diverse students. 
Mar 14    Homework 6  Homework 6 discussion.
Equations. The concept of equation. Questions. 
Mar 16  10:0011:30 AM, PB 011, 012, 013. Math Circle, grades 49  observers welcome.  
Mar 19      Polynomials. Polynomial equations. Roots and graphs of polynomials. Solving polynomial equations and inequalities.
Overleaf file with this discussion. 
Mar 20  6:008:00 PM, S2 308. Math Circle, grades 1012  participants welcome.  
Mar 21    Homework 7  Homework 7 discussion.
Review: Study Guide and Sample Problems 
4:458:15 PM, IT 290, EE 188. Math Kangaroo Competition, grades 112  helpers needed.  
Mar 26  Spring break  
Mar 28  Spring break  
Apr 2      Test 2 (on topics from Natural Numbers to Equations). 
Apr 3  5:307:30 PM, PB 013. Math Circle, grades 912  participants welcome.  
Apr 4    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. 
Apr 6  10:00 AM12:00 PM, PB 011, 012, 013, 103. Math Kangaroo Solutions and Awards, grades 112  leaders needed for grades 34, 56, 78, one helper needed for grades 12.  
Apr 9      Algebraic structures. Definitions: group, abelian group, ring, commutative ring, field. Chart of groups through fields. 
5:307:30PM, S2 206 (grades 68), S2 109 (grades 912). Math Field Day practice, grades 68  leaders needed, grades 912  participants welcome.  
Apr 11    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 13  10:0011:30 AM, PB 011, 012, 013. Math Circle, grades 49  observers welcome.  
Apr 16      Similarity. Areas and volumes of similar figures/solids.
Math club problems. More problems on similarity. 
Apr 17  6:008:00 PM, S2 308. Math Circle, grades 1012  participants welcome.  
Apr 18    Homework 9  Homework 9 discussion. Proportional reasoning.
Discussion on Service Learning: mathematics in everyday life. 
Apr 20  approx. 8:00AM4:30 PM, various locations on campus. Math Field Day, grades 612  helpers needed.  
Apr 23      Math Field Day games. Final Project 
Apr 25    Homework 10  Homework 10 discussion.
Review: Study Guide and Sample Problems 
Apr 27  10:0011:30 AM, PB 103, 105, 106. Math Circle, grades 49  observers welcome.  
Apr 30      Test 3 (on topics from Polynomials to Similarity). 
May 1  6:008:00 PM, S2 308. Math Circle, grades 1012  participants welcome.  
May 2      Presentations: Service Learning 
May 7      Presentations: Service Learning (cont.)
Discussion on Service Learning: how did our work benefit the students and the community? 
May 9  Faculty consultation day. Consultation hours: 10:3011:30 AM in PB 340 for all classes, 2:003:15 in S 139 for Math 149S only  
May 10  Faculty consultation day. Consultation hours: 3:004:00 PM in PB 340 for all classes  
May 16      Final Project due 11:59 PM. 