CRN 13278

• Time and Place. TR 13:30-14:50 in LART 206 MAIN 306

• Instructor. Helmut Knaust, Bell Hall 219, hknaust@utep.edu, 747-7002

• Office Hours. T 15:00-16:20, R 8:30-10:20, or by appointment.

• 
  Textbook. Zalman Usiskin, Anthony L. Peressini, Elena Marchisotto, and Dick Stanley. Mathematics for High School Teachers- An Advanced Perspective. Prentice Hall. Amazon.com sells the paperback edition for $54.46 (8/11/09). The textbook is required at all class meetings, and the parts covered in class are intended to be read in full.

• Course Requirements.
  • Quizzes (15%): I will give regular, but unannounced quizzes. Quiz problems will be identical to prior homework assignments. Your worst two quizzes will be dropped.
  • Exams (25%): You will have two in-class exams on the following days: Thursday, October 8 and Tuesday, November 24.
  • Class Presentations (25%): Groups of students will design and conduct all classroom activities for two or more sessions and will be responsible for the content covered in those sessions. Each group will also create homework assignments and will design appropriate quiz questions. This work will require both individual and group work and will be evaluated in both of those ways.
    • NOTE: The groups will meet with me two weeks before your presentation so that I will know you are prepared. This is not optional. If you do not meet with me, you will lose half of your possible points.
  • Final Project (25%): There are mathematics problems that require more attention than just one day. Some of these problems are found at the end of the chapters in the textbook. Student groups will complete one of the problems and present their results in class at the end of the semester.
  • Class Participation (10%): Mathematics is not a spectator sport. During class I expect you to participate. This is an active class where students often present solutions to their peers. The participation grade will be based both on the quality and frequency of your contributions.

• Grades. Your grade will be based on the percentage of the total points that you earn during the semester. You need at least 90% of the points to earn an A, at least 80% for a B, at least 70% for a C, and at least 60 % for a D.

• Make-up Exams. Make-up tests will only be given under extraordinary circumstances, and only if you notify the instructor prior to the exam date. There will be no make-up quizzes.

• Time Requirement. I expect that you spend an absolute minimum of six hours a week outside of class on reading the textbook, preparing for the next class, reviewing your class notes, and completing homework assignments. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.

• Attendance. You are strongly encouraged to attend class every day. I expect you to arrive for class on time and to remain seated until the class is dismissed. Students with five or more absences (excused or unexcused) will be dropped from the course with a grade of "F".

• Drop Policy. The class schedule lists Friday, October 30, as the last day to drop with an automatic "W". After the deadline, I can only drop you from the course with a grade of "F". Beginning with the fall 2007 semester, all freshmen enrolled for the first time at any Texas public college or university will be limited to six course withdrawals (drops) during their academic career. Drops include those initiated by students or faculty and withdrawals from courses at other institutions! This policy does not apply to courses dropped prior to census day or to complete withdrawals from the university.

• Students with Disabilities. If you have a disability and need special accommodation, please contact the Disabled Student Services Office (DSSO) in Union East 106, 747-5148, dss@utep.edu.

• Academic Integrity. All students must abide by UTEP's academic integrity policies, see http://academics.utep.edu/Default.aspx?tabid=23785 for details.

Homework

• 12/3/09 Final Projects - presentation.
• 12/1/09 Work on final projects in class.
• 11/24/09 Test 2.
• Extra office hours: Friday 11/20/09, 10:00-12:00; Monday 11/23/09, 15:00-17:00.
• 11/17/09: Read 4.3.3. Prepare 4.3.3: 4a-c,7,13a.
• 11/12/09: Read 4.3.2. Prepare 4.3.2: 1a-f,2.
• 11/10/09: Read 4.2.3, 4.3.1. Prepare 4.2.3: 1ac,2. 4.3.1: 2,3,5.
• 11/5/09: Read 4.2.2-4.2.3. Prepare 4.2.2: 1c,3,6,7. 4.2.3: 1ac,2.
• 11/3/09: Read 3.2.2. Prepare 3.2.2: 2,6a,7,8,9c,13.
• 10/29/09: Read 3.2.1. Prepare 3.2.1: 3ab,6,11.
• 10/27/09: Read 4.1.2-4.2.1. Prepare 4.1.2: 1,2,3,8,16. 4.2.1: 2,3a-d.
• 10/22/09: Read 4.1.1-4.1.2. Prepare 4.1.1: 3,8,9. 4.1.2: 1,2,3,8,16.
• 10/20/09: Read 3.1.3-3.2.1. Prepare 3.1.3: 3,4,9.
• 10/15/09: Read 3.1.2-3.1.3. Open problems: 3.1.1: 8,9; 3.1.2: 6a-f.
• 10/13/09: Read 3.1.2-3.1.3. Prepare 3.1.2: 6a-f.
• 10/8/09 Test 1.
• 10/5/09: Extra office hours 10:00-12:00, 14:00-17:00.
• 10/1/09: Read 3.1.1,3.1.2. Prepare: 3.1.1: 1,2,5,6,8,9.
• 9/29/09: Split into groups of four students - Turn in sheet with the names on Thursday. Read 3.1.1-3.1.2.
• 9/24/09: Finish Worksheet 4. Open Problems: 2.2.1: 1bdef,2b,4. 2.2.2: 3,4,6,13,15.
• 9/22/09: Read 2.2.2, 3.1.1. Prepare: 2.2.2: 3,4,6,13,15.
• 9/17/09: Read 2.2.1-2.2.2. Prepare: 2.2.1: 1bdef,2b,4.
• 9/15/09: Open problems: 2.1.2: 8. 2.1.3: 5,6,8. 2.1.4: 3,4,5b,6.
• 9/10/09: Read 2.1.4-2.2.1. Prepare: 2.1.4: 3,4,5b,6
• 9/8/09: Read 2.1.3-2.1.4. Prepare: 2.1.2: 8. 2.1.3: 1,2,3a,4,5,6,8.
• 9/3/09: Read 2.1.2.-2.1.3. Prepare: 2.1.2: 1,4,6,8.
• 9/1/09: Read 2.1.1.-2.1.3. Prepare: 2.1.1: 1,3,8,9,10,12. 2.1.2: 1,4,6,8.
• 8/27/09: Read 2.1.1.-2.1.3.
• 8/25/09: Read Chapter 1. Prepare Ex. 1.2,1.4,1.6,1.11.

Materials

• Final Projects
• Student Presentations
• Quiz 4 (Solutions) | Cognitive Demands II | Cognitive Demands I | Worksheet 4 | Worksheet 3 | Worksheet 2 (Version 2) | Worksheet 2 | Worksheet 1
• InverseCubic.nb |Complex.nb | Riemann.nb | Roots.nb | CheapCalculator_II.nb | CheapCalculator.nb | BabylonianAlgorithm.nb | FactoringIntegers.nb | DecimalRepresentation.nb | Leibniz.nb | Remote access to Mathematica
• Curriculum Frameworks developed by the El Paso Collaborative for Academic Excellence: Algebra I | Geometry | Algebra II | Precalculus
• Sluggish Results Seen in Math Scores, by Sam Dillon (NYT, 2009/10/14):

Eighth graders, on average, scored 283 on the same scale, up from 281 in 2007. White eighth graders, on average, scored 293, while Hispanics scored 266 and black eighth graders scored 261. The gap of 32 points separating average black and white eighth graders represents about three years’ worth of math learning.

References

• Edward B. Burger & Robert Tubbs, Making Transcendence Transparent: An intuitive approach to classical transcendental number theory. Springer-Verlag, 2004.

An introduction to transcendental number theory, at the advanced undergraduate/beginning graduate level.

• Heinz-Dieter Ebbinghaus et al., Numbers. Springer-Verlag, 1996.

Real numbers, complex numbers, quaternions - what's next? The first part of the book is quite accessible, but the going gets tougher in the later chapters.

• Edmund Landau, Grundlagen der Analysis. (Also available in English as Foundations of Analysis.) AMS Chelsea Publishing.

A classic written in the 1920s. An axiomatic construction of numbers and concise derivation of their fundamental properties, from the natural numbers to the complex numbers.

• Serge Lang, Basic Mathematics. Addison Wesley, 1971.

Serge Lang wrote more than 50 books. This is the prolific author's treatise on high school mathematics.

• Liping Ma, Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States. Lawrence Erlbaum Associates, 1999.

...Ma has done a masterful job of showing how the conceptual approach of Chinese elementary school teachers succeeds where the procedural approach of their American counterparts flounders....I highly recommend this brief volume to elementary school teachers who wish to improve their teaching of mathematics... (Mathematics Teaching in the Middle Schools)

• Gary Martin, Focus in High School Mathematics: Reasoning and Sense Making. National Council of Teachers of Mathematics, 2009.

Executive summary.

• Ivan Niven, A simple proof that π is irrational. Bull AMS 53 (1947), 509.

Only about half a page...

• Tristan Needham, Visual Complex Analysis. Oxford University Press, 1999.

A unique book developing complex analysis from a geometric angle.