Math 4050.002: Spring 2012
Meets: MWF 9:00-9:50 in GAB 317.
Instructor: Professor John Quintanilla
Office: GAB, Room 418-D
Office Phone: x4043
E-mail: jquintanilla@unt.edu
Web page: http://www.math.unt.edu/~johnq/Courses/2012spring/4050/
Office Hours: T 10-12, W 10-12, or by appointment. I'm fairly easy to find, and you're welcome to drop by outside of office hours without an appointment. However, there will be occasions when I'll be busy, and I may ask you to wait or come back later.
Required Text: Mathematics for Secondary School Teachers, by E. G. Bremigan, R. J. Bremigan, and J. D. Lorch. Course topics are chosen to ensure all TNT math majors are exposed to the topics listed in the program standards for initial preparation of secondary mathematics published by the National Council of Teachers of Mathematics. Course topics are also chosen to ensure that your future students are prepared for the mathematics portion of the Texas College and Career Readiness Standards.
Strongly Recommended: Lecture notes for the semester are available at the UNT Copy Center for approximately $12.
Prerequisite: Math 3000.
For Your Information: Dates and other information about the practice state certification exam may be found at http://www.coe.unt.edu/texes. Another good (and free) resource for preparing for the state certification exam is T-CERT. Information about the real TExES Mathematics 8-12 certification exam can be found by following the link.
The
following chapters and sections of the textbook will be covered according to
the projected schedule below. Dates may change as events warrant.
- Chapter 4: Trigonometry
- 4.5: Trigonometry,
Coordinate Geometry, and Linear Algebra
- 4.5.3: Complex
multiplication
- Chapter 7: Operations in Number Systems
- 7.6: Complex Numbers
- 7.6.3: Polar
decomposition
- 7.6.4: The geometric
meaning of complex multiplication
- Chapter 8: Topics in Number Systems
- 8.1: Arithmetic in the
Integers
- 8.1.1: Divisors and
multiples
- 8.1.2: Greatest common
divisors and least common multiples
- 8.1.3: Primes
- 8.1.4: The Fundamental
Theorem of Arithmetic
- 8.1.5: Applications of
FTA
- 8.1.6: The Division
Algorithm
- 8.2: Systems of
Numeration for Whole Numbers
- 8.2.3: Hindu-Arabic
numeration
- 8.3: Divisibility Tests
- 8.3.1: Familiar tests
and their proofs
- 8.4: Decimals
- 8.4.1: Making sense of
decimals
- 8.4.2: Some
technicalities
- 8.4.3: Rational versus
irrational numbers and their decimal expansions
- 8.5: Algebraic and Transcendental
Numbers
- 8.5.1: Definitions and
examples
- Chapter 9: Exponentiation
- 9.1: Whole Number
Exponents
- 9.1.1: Shorthand for
repeated multiplication
- 9.2: Integer Exponents
- 9.2.1: Non-positive
exponents
- 9.2.2: Properties of
exponentiation with integer exponents
- 9.3: Rational Exponents
- 9.3.1: Roots and
dueling notations
- 9.3.2: Rational
exponents: roots and powers of the base
- 9.4: Real Exponents
- 9.4.1: The real
exponential functions
- 9.5: The Real
Logarithmic Functions
- 9.5.1: The logarithm:
definition and properties
- Chapter 10: Exponential and Logarithmic Functions:
History, Computation, and Application
- 10.1: Logarithms and
History: Logarithm Tables
- 10.1.1: Logarithm
tables and interpolation
- 10.2: Logarithms and
History: The Natural Logarithm
- 10.2.1: The natural
logarithm: if it looks like a logarithm then it probably is one
- 10.2.2: Estimating
natural logarithms
- 10.3: Compelling
Properties of the Natural Logarithm and Natural Exponential Function
- 10.3.1: Logarithms
with base a,
revisited
- 10.3.2: Inverse functions
and their derivatives; the derivative of exponential functions
- 10.3.3: More on the
number e
- 10.3.4: Summary
- 10.4: Applications of
Exponential Functions
- 10.4.1: Exponential
growth
- 10.4.2: Compound
interest
- Chapter 11: Transcendental Functions and Complex
Numbers
- 11.2: Roots of Complex
Numbers
- 11.2.1: Examples of
roots
- 11.2.2: Main results
- 11.2.3: Principal
roots
- 11.3: Rational
Exponents: Roots and Powers of the Base
- 11.3.1: Problems
arise: negative and complex bases
- 11.4: The Complex
Exponential Function
- 11.4.1: Definition
- 11.4.2: Additive
property of exponents
- 11.4.3: Euler’s
Formula: writing ez
in terms of familiar functions
- 11.4.4: The complex
logarithm
- 11.5: Complex Bases and
Complex Exponents
- Chapter 12: Beyond Quadratics: Higher Degree Polynomials
- 12.2: Connections:
Roots and Coefficients
- 12.2.1: Conjugate
roots
- 12.2.2: Rational Roots
Theorem
- 12.2.3:
Descartes’ Rule of Signs
- 12.4: Factoring and the
Fundamental Theorem of Algebra
- 12.4.1: Fundamental
questions lead to a fundamental theorem
- 12.4.2: Division
algorithm and factor theorem
- 12.5: Application:
Newton’s Method and Polynomials
- 12.5.2: Newton’s
method, polynomials, and the Remainder Theorem
|
January
18: 8.1.6 |
January
20: Q/A |
|
|
January
23: 8.1.1,
8.1.2, 8.1.6 |
January
25: 8.1.3,
8.1.4 |
January
27: Q/A |
|
January
30: 8.1.4,
8.1.5 |
February
1: 8.2.3 |
February
3: Q/A |
|
February
6: 8.3.1,
8.4.1, 8.4.2 |
February
8: 8.4.3 |
February
10: Q/A |
|
February
13: Review
|
February
15: Exam
#1 |
February
17: Q/A |
|
February
20: 8.4.3 |
February
22: 7.6.2 |
February
24: Q/A |
|
February
27:
12.4.2, 12.5.2 |
February
29:
12.2.2, 12.4.2 |
March
2: Q/A |
|
March
5: 12.2.1 |
March
7: 12.4.1 |
March
9: Q/A |
|
March
12: Review |
March
14: Exam
#2 |
March
16: Q/A |
|
SPRING BREAK |
||
|
March
26:
Graphing polynomials |
March
28: 8.5.1 |
March
30: Q/A |
|
April
2: 9.1,
9.2, 10.4.2 |
April
4: 9.3.2,
9.4.1 |
April
6: Q/A |
|
April
9: 9.5.1,
10.1.1 |
April
11:
10.2.1, 10.3.1, 10.3.2 |
April
13: Q/A |
|
April
16: Review
|
April
18: Exam
#3 |
April
20: Q/A |
|
April
23:
10.2.2, 10.3.3, 10.3.4, 10.4.1 |
April
25: 4.5.3,
7.6.4, 11.2.1 |
April
27: Q/A |
|
April
30: 11.2,
11.3, 11.4, 11.5 |
May
2: Review |
|
|
|
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May
11: Final:
8:00-10:00 |
Student Responsibilities
- You should read over this syllabus carefully, as I will
hold you responsible for the information herein.
- Students will be expected to read the chapters
carefully, including the examples in the book.
- Students will be responsible for obtaining any and all
handouts. If you are not in class when handouts are given, it is your
responsibility to obtain copies.
- You should begin working now. Frequent practice is
crucial to the successful completion of a mathematics course. Cramming at
the last minute will certainly lead to failure.
- WARNING: If you are in academic trouble, or are in danger of
losing your financial support, or if your parent or guardian is expecting
a certain grade at the end of the semester... start working today. I will
refuse to listen to any pleas at the end of the semester. You will receive
precisely the grade that you earn.
Grading Policies
The following schedule is tentative and is subject to capricious changes in case of extracurricular events deemed sufficiently important to the upper administration.
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Cooperation is encouraged in doing the homework assignments. However, cheating will not be tolerated on the exams. If you are caught cheating, you will be subject to any penalty the instructor deems appropriate, up to and including an automatic F for the course.
Attendance is not required for this class. However, you will be responsible for everything that I cover in class, even if you are absent. It is my experience that students who skip class frequently make poorer grades than students who attend class regularly. You should consider this if you don't think you'll be able to wake up in time for class consistently.
The grade of "I" is designed for students who are unable to complete work in a course but who are currently passing the course. The guidelines are clearly spelled out in the Student Handbook. Before you ask, you should read these requirements.
Exam Policies
- Unless announced otherwise, calculators will not
be permitted for use on exams.
- I expect to give exams during the weeks above. However,
these are tentative dates. I will announce the exact date of each exam in
class.
- After exams are returned in class, you have 48 hours to
appeal your grade. I will not listen to any appeals after this 48-hour
period.
- I will not drop the lowest exam score; all will count
toward the final grade.
- No make up exams will be
given. For those students who miss an exam due to an Authorized Absence
(see the Student Handbook), the final grade will be computed based
only on those exams taken, together with homework/quiz scores and the
final exam. Such students will be required to provide official written
verification of such an absence.
- Students missing an exam for unauthorized reasons will
receive 0 (zero) points on the exam.The Final
Examination will be comprehensive in the sense that problems may come from
any of the sections that will be covered during the semester.
- The grade of A signifies consistent excellence
over the course of the semester. In particular, an A on the final is not
equivalent to an A for the course.
- I reserve the right to test and quiz you on problems
which are generalizations of material covered in the class and/or in the
text. In short, the problems may not look exactly like the ones in the
book.
- Everything that I say in class on Mondays and
Wednesdays is fair game for exam material. You will be responsible for
everything unless I advise you to the contrary.
- You will not be held responsible for the
certification exam preparations, Friday presentations, or the two class
projects on the exams.
Homework Policies
- Homework will be assigned every Friday and will be due the following Friday. All assignments will be posted online.
- Most weeks, you will be expected to work on four different assignments at once: (1) homework based on the Monday/Wednesday lectures, (2) preparation for the TExES Mathematics 8-12 certification exam, (3) Friday presentations, and (4) two different class projects.
- I expect the assignments that you turn in to be written up carefully and neatly, with the answers
clearly marked. You must show all of your work. Messy homework will not
be accepted.
Homework based on the Monday/Wednesday lectures
- Entire homework assignments will not be graded.
Instead, only five representative problems will be graded per assignment.
As a consequence, it will be possible to not do the entire assignment and
still receive a perfect score on that particular assignment. Deliberately
leaving homework uncompleted is highly unrecommended,
however, as the law of averages will surely catch up with you as the
semester progresses.
- When computing grades, I will drop the two
lowest homework grades before computing the homework average. Therefore,
in principle, you could get a 100% homework score and also not turn in two
assignments during the semester. I have this policy in case you get sick, a family emergency arises, etc., during the
semester. You will still be responsible for the material in such assignments
during the examinations.
- Because of this policy, I will not give
extensions on homework assignments, nor will I accept late assignments.
Certification exam preparation
- Every week, you will be given about 12-18 problems on
topics pertinent to the Mathematics 8-12 certification exam. These are
mostly chosen from problems that appeared on Precalculus
and Calculus I exams given by your instructor to TAMS students in past
years.
- For each assignment, you will also choose 5 problems
from the remaining preparation problems. If you submit more than five such
problems, the grader will simply grade the first five problems on the
homework assignment.
- When computing grades, I will drop the two
lowest grades before computing the certification exam preparation average.
Because of this policy, I will not give extensions on the
certification assignments, nor will I accept late assignments.
Friday presentations
- Every week, selected problems from a collection of hard questions from real high school
students will be posted. Every Friday, students will be sent to the
board, one at a time in random order, to demonstrate how they would answer
these questions if posed by a future high school student.
- With these presentations, you should develop two
important skills: solidifying your content knowledge of secondary
mathematics and learning how to "sell" difficult ideas to your
future students.
- All presentations will be peer graded.
- If you get called to the board on a Friday but have an
unexcused absence, you will get a 0 for this presentation.
- All presentation grades will be used to compute the
Friday presentations average.
- If you really mess up on a presentation --- or are
called to the board on a day that you miss class --- you are permitted
once during the semester for a second-chance session to be scheduled with
your instructor. At such a session, you will be asked to be prepared to answer
about ten of these questions, actually answer maybe three or four, and
will be directly assessed by your instructor.
Class projects
- There will be two different class projects assigned in
this class.
- The first class project concerns developing ideas to
sell course content to high school students that may not like mathematics
as much as you do.
- The second class project concerns differentiated
instruction. The primary goal
of this project is for you to analyze students’ work and decide on
next steps based on that work.
Final Notes
- For the sake of completeness, I list some other areas
that new teachers struggle with, according to experienced secondary
teachers:
- Being willing to seek
advice from seasoned instructors
- Covered the whole
curriculum over the course of a year without getting bogged down on
specific topics
- Classroom management
- Keeping appropriate
documentation (e.g., special-needs students, communication with parents,
etc.)
- Appropriate use of
classroom technology
- Being consistent in
enforcing discipline
- Keeping authority
(i.e., not just being a pal to one's students)
- Maintaining
professional distance
- In compliance with the Americans with Disabilities Act,
I mention the following: It is the responsibility of students with
certified disabilities to provide the instructor with appropriate
documentation from the Dean of Students Office.