Math 3000
Introduction to Abstract Math
Fall 2011
Instructor: Mike Ferrara
Office: CU 607
Office Phone: (303) 556-8460
E-mail: michael.ferrara@ucdenver.edu
Website: math.cudenver.edu/~mferrara
Office Hours: Tu/W: 9:30-11
(Class) Room: Plaza 146
Meeting Times: M/W 3:30-4:45
Description: An introduction to the fundamentals of advanced mathematics,
particularly techniques of proof. Other topics include set theory, elementary symbolic
logic, functions and relations.
Prerequisite: Knowledge of elementary mathematics, including calculus and algebra.
Corequisite: None.
Textbook: Mathematical Proofs: A Transition to Advanced Mathematics, 2nd edition.
Chartrand, Polimeni, Zhang.
Expectations: Understanding of the material in this course is crucial for success in
upper-division mathematics courses. As such, the demands made of students are high.
Certain students will grasp the material faster than others, and as such the time
expectations may vary. Students can expect to spend around 5-6 hours per week on
HW assignments as well as devoting time to learning definitions and understanding
concepts.
As you progress in your mathematical studies, time spent reading textbooks will likely
increase. This class is no different – please be open to reading the textbook, handouts
and your notes prior to jumping into the HW.
You can also expect several things from me, the foremost of which is my support of all
of your efforts in the course. While I feel that struggle is an important part of learning
advanced mathematics, you are not expected to struggle alone – I am here to help you
along the way. I will also do all that I can to get your assignments graded and returned
within 1 week, if not sooner when I can.
Grading: Homework (35%) Homework problems will be assigned each week (see
Blackboard for a complete list). Students must show all work receive credit for an
assignment. Proofs must be composed of complete sentences, and clarity is an
important aspect of a completed HW assignment. HW will be assigned at the end of
each week (generally Wednesday or Thursday) and is due the Wednesday of the week
after it is assigned.
I will frequently assign homework problems that are somewhat different than
the problems covered in class (although there will be plenty of similar problems as well).
Conceptual understanding often begins, but seldom completely achieved, through
mimicry. This makes the above comment about spending time reading the notes and
textbook separate from your HW even more critical.
Quizzes: (5%) This class is, in part, where you learn the “language” of mathematics, and
success in the course will depend heavily on reading, understanding and knowing key
terminology. There will be periodic, and unannounced, terminology/concept quizzes
throughout the semester. The first quiz will not be given prior to the third week of
class.
Proofs “Labs”: (10%) There are two “Lab Weeks” scheduled during the semester. You
are permitted to complete the proof labs in groups of up to, but not exceeding, four
students. Each lab will last approximately 2 hours, with time for group work. The labs
will also have a written component that is to be handed in roughly one week after the
lab.
Midterm: (20%) The midterm exam will be administered on 10/26/11.
Final Exam: (30%) The final exam will be comprehensive. While the final may be slightly
more focused on the material from the latter half of the semester, mastery of all course
material will be necessary for success on the final.
Late Assignment Policy: Any student that misses an exam without notifying me before
the exam begins will receive a grade of '0'. Please note that notifying me is not
sufficient to assure a make-up exam, as they are rare. The final exam is in-class, and if
you are not present, you will receive a zero. Plane tickets, weddings, etc. are not
acceptable reasons to miss the final.
Homework must be handed in no later than the end of class on the day it is due. If you
feel that there is a reason you will not be able to hand a HW in at that time, you must
speak to me (or email me) before the class when the HW is due.
Academic Dishonesty:
Academic dishonesty is a serious offense at the University because it diminishes the
quality of scholarship and the learning experience for everyone on campus. An act of
Academic Dishonesty may lead to sanctions including a reduction in grade (up to and
including a permanent F for the course), probation, suspension, or expulsion. Academic
dishonesty includes cheating, fabrication, plagiarism, submitting the same paper or
work for more than one class, and facilitating academic dishonesty. For definitions and
more information, see the CLAS website:
http://www.ucdenver.edu/academics/colleges/CLAS/facultystaff/policies/Pages/AcademicIntegrity.aspx
Drops and Incompletes:
Incomplete grades (IW or IF) are NOT granted for low academic performance. To be
eligible for an incomplete grade, students MUST (1) successfully complete a minimum of
75% of the course, (2) have special circumstances beyond their control that preclude
them from attending class and completing graded assignments, and (3) make
arrangements to complete missing assignments with the original instructor via
completion of a CLAS Course Completion Agreement. Verification of special
circumstances is required. The CLAS Course Completion Agreement is available from
the CLAS Advising Office, NC 2024 or from the Department of Mathematics.
Sections Covered: May be rearranged/altered at instructor’s discretion.
Week of:
August 22nd
August 29th
September 5th
September 12th
Topics Covered
Elementary Logic
Direct Proofs;
Contrapositive;
Elementary Number
Theory (Divisibility and
Congruence)
Elementary Number
Theory, Continued
An introduction to
basic set theory;
Proofs Involving Sets
Book Sections
2.1-2.4
3.1, 3.2
Notes
2.4, 3.2
3.3
4.1, 4.2
Parts of Chapter 1
4.3
September 19th
Proofs Involving Sets;
Review of Negation
September 26th
Proof by Contradiction
4.4+
October 3rd
Counterexamples and
Contradiction;
5.1, 5.2
No Class
9/5/2011
Labor Day
Existence
October 10th
Induction
October 17th
Induction**
October 24th
Relations; Midterm
Properties of
Relations;
Equivalence Relations
October 31st
November 7th
November 14th
November 21st
November 28th
December 5th
Equivalence Relations;
Order Relations;
Functions
Types of Functions;
Composition of
Functions
Fall Break
Composition of
Functions;
Inverse Functions;
Cardinality
Cardinality
Chapter 6;
Supplemental
Material
Proof Lab #1 This
Week
Chapter 6;
Supplemental
Material
8.1; 8.2
**: Last material
on Midterm;
8.2, 8.3, 8.4
Proof Lab #1 Due
11/2
8.4,
Supplemental
Material, 9.1
Proof Lab #2 This
Week
Midterm 10/26
9.3, 9.4
To-GA!
To-GA!
9.4, 9.5, 10
Proof Lab #2 Due
11/30
Parts of Chapter 10
Fall 2011 CLAS Academic Policies
The following policies pertain to all degree students in the College of Liberal Arts and
Sciences (CLAS).
 Schedule verification: It is each student’s responsibility to verify online that
his/her official registration is correct: verify before classes begin and prior to
the drop/add deadline. Failure to verify schedule accuracy is not sufficient
reason to justify a late add or drop.
 E-mail: Students must activate and regularly check their official student email account for CU Denver business: http://www.ucdenver.edu/studentservices/Pages/WebMail.aspx. Those who forward email to a private account
are still responsible for checking their official student e-mail account for
messages not automatically forwarded.
 Waitlists:
 Students are not automatically notified if they are added to a class from a
waitlist. Students are not automatically dropped from a class if they
never attended, stopped attending, or do not make tuition payments.
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Waitlists are purged after the 1st week of classes, after which a paper
Schedule Adjustment Form (drop/add form) is required. It is the
student's responsibility to get the form (online or at the Advising Office,
NC 4002), have it signed, deliver it to the Registrar (Annex 100) or the
Student Services Center (NC 1003), and verify her/his schedule online.
Late adds (after 7 September) will be approved only when circumstances
surrounding the late add are beyond the student’s control. This will require a
written petition and verifiable documentation. Petition forms are available in
NC 4002. The signature of a faculty member on a Schedule Adjustment Form
does not guarantee that a late add petition will be approved.
Late drops (after 14 November) will be approved only when circumstances
surrounding the late drop have arisen after the published drop deadline and
are beyond the student’s control. This will require a written petition and
verifiable documentation. The signature of a faculty member does not
guarantee that a late drop petition will be approved.
Tuition: Students are responsible for completing arrangements with
financial aid, family, scholarships, etc. (depending on tuition plan selected) to
pay their tuition prior to Census Date (7 September). Students who drop after
that date are (1) financially responsible for tuition and fees, (2) academically
responsible and will receive a "W" grade, and (3) are ineligible for a refund of
COF hours or tuition.
Graduation:
 Undergraduate students wishing to graduate in fall 2011 must complete
the online Intent to Graduate Form and meet with their academic advisor
to obtain a graduation application. This application must be submitted by
Census Date (7 September). You can obtain an application only after
meeting with your advisor. There are no exceptions to this policy.
 Graduate students wishing to graduate in fall semester 2011 must
complete the online Intent to Graduate form and have a Request for
Admissions to Candidacy on file with the CU Denver Graduate School
(Lawrence Street Center) no later than 5 PM, September 7, 2011.
Important Dates and Deadlines
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August 22, 2011: First day of classes.
August 28, 2011: Last day to add a class or be added to a waitlist using the
UCD Access student portal. After this date, you must use a Schedule
Adjustment Form to change, add, or drop.
August 29, 2011: LAST DAY TO DROP WITHOUT DROP CHARGE – THIS
INCLUDES SECTION CHANGES.
August 29, 2011: Waitlists are dropped. Any student not added to a course
automatically from the waitlist by this date MUST complete a Schedule
Adjustment Form to be added. Students are NOT automatically added to the
class from the waitlist after this date and time. If your name is not on the
official student roster, you are not registered for the course.
August 30-September 7, 2011: Students are responsible for verifying an
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accurate fall 2011 course schedule via the UCDAccess student portal.
Students are NOT notified of their waitlist status by the University. All
students must check their schedule prior to 9/7 for accuracy.
August 30, 2011: First day instructor may approve request to add a student
to a course with a Schedule Adjustment Form.
September 7, 2011: Census date.
 9/7/11, 5 PM: Last day to add structured courses without a written
petition for a late add. This is an absolute deadline and is treated as such.
This deadline does not apply to independent studies, internships, project
hours, thesis hours, dissertation hours, and late-starting modular courses.
 9/7/11, 5 PM: Last day to drop a fall 2011 course or completely
withdraw from all fall 2011 courses using a Schedule Adjustment Form
and still receive a tuition refund, minus the drop fee. After this date,
tuition is forfeited and a "W" will appear on the transcript. This includes
section changes. This is an absolute deadline and is treated as such.
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9/7/11, 5 PM: Last day to request pass/fail or no-credit option for a
course.
9/7/11, 5 PM: Last day for a graduate student to register for a Candidate
for Degree.
9/7/11, 5 PM: Last day for a Ph.D. student to petition for a reduction in
hours.
9/7/11, 5 PM: Last day to apply for fall 2011 graduation. You must make
an appointment and see your academic advisor before this date to apply
for graduation if you are an undergraduate; you must complete the Intent
to Graduate and Candidate for Degree forms if you are a graduate student.
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September 19-28, 2011: Faculty can use the Early Alert system.
October 31, 2011, 5 PM: Last day for non-CLAS students to drop or
withdraw without a petition and special approval from the academic dean.
After this date, a dean’s signature is required.
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November 14, 2011, 5 PM: Last day for CLAS students to drop or withdraw
with signatures from the faculty and dean but without a full petition. After
this date, all schedule changes require a full petition. Petitions are available in
NC 4002 for undergraduates and in the CU Denver Graduate School offices for
graduate students.
November 21-27, 2011: Fall break (no classes; campus closed). Be thankful.
December 12-17, 2011: Finals Week. No schedule changes will be granted
once finals week has started. There are NO exceptions to this policy.
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December 27, 2011: Fall final grades available on UCD Access (tentative).