Course Information

Math 311: Introduction to Proof and Abstract Mathematics – Section 01, Fall 2015

3 Credits: MTWHF 9:00am – 9:50am Bridges Room 261

Class Meeting Dates: Monday, October 26th – Tuesday, December 8th

 

Textbook: Discrete Mathematics and Its Applications, 7th ed, by Kenneth H. Rosen [Required]

Office: MacLean 375M                               Office Phone: (218)477-4011

Office Hours:  MTWHF 10:00am – 10:50am    Email:  jamesju@mnstate.edu

MTWHF 11:00am – 11:50am                              Webpage:  web.mnstate.edu/jamesju

                                      Other times by Appointment

 

Course Description:  Methods of proof, include direct and indirect methods, mathematical relations and properties of relations, and an axiomatic treatment of Boolean Algebras.                Pre-requisite:  MATH 210 – Concepts from Discrete Mathematics.

 

Course Requirements: The primary purpose of this course is to introduce you to the basic techniques and methods used to write mathematical proofs.  Unlike many of your previous experiences with mathematical proofs, this course is not designed to be a spectator sport.  While watching your instructor do model proofs can be helpful as a starting point, the best way to learn to write proofs is to actively explore the related concepts and ideas, to build intuition by working out special cases or motivating examples, to bounce ideas off of your classmates, and to write, rewrite, present, revise, and perfect your own proofs.  Since every mathematical proof is about some aspect of mathematical content, we will also learn or revisit a fair amount of related mathematical content along the way, but developing our proof-writing abilities will be the central concern of this course.

 

 

Major Content Areas:

·        Defining properties of Boolean algebra

·        Equivalence relations

·        Partial orderings

·        Proof methods and strategies

·        Proofs of properties of Boolean algebras

·        Relations and the properties of relations

·        Representations of relations

·        Rules of inference and an introduction to proofs

 

Student Learning Outcomes:

·        Understand basic notions of relations, equivalence relations, partial orderings, and partitions.

·        Understand the axiomatic nature of mathematics.

·        Prove formal results in Boolean algebras.

·        Prove a variety of results using direct and indirect proofs.

 

 

Instructional Strategies:  Lecture, discussion, group activities, presentations, proof portfolios, projects.

 

Attendance and Academic Expectations:  Since discussion, in class activities, group work, and proof presentations are all key components of the design of this course, attending class regularly is of paramount importance.  I will not directly penalize your grade for absences, but those who miss a group activity will be required to complete an alternate assignment in order to make up for any in-class assignments that they missed.  Also, just to be clear, each student in the class will be expected to do at least one short in class presentation of a proof or problem sometime during the semester.  This is not optional.  Lastly, no one is born knowing how to write good mathematical proofs – it is a learned skill that can be developed and perfected with practice, effort and dedication.  By helping one another and maintaining a positive attitude and environment in the classroom, my hope is that each one of you will leave the class more confident in your ability to write mathematics proofs and to engage in mathematical reasoning and problem solving.

 

Homework/Quizzes and Activities: I will collect and grade book homework problems several times during the course.  When I do, you will be told at least 2 days in advance which problems you are expected to turn in.  However, traditional book problems will not play as large a role in this class as they did in Math 210.  I also will give quizzes at various times during the course.  I typically announce quizzes one class period before I give them so you have time to prepare for them.  Quizzes will be worth from 5-10 points, depending on their length and scope.

 

There will also be several in class activities.  Some will be collected at the end of class.  Others can be taken home and completed prior to a future class session. 

 

Your homework, quiz, and activity scores will be combined to contribute 125 points toward your final grade.  There should be enough of these assignments that a few can be dropped.

 

Projects: There will be several opportunities to do projects during the course.  The length, scope, and point value of projects will vary.  There should be more than 50 points worth of projects during the course, so you will have some freedom in choosing which projects you would like to work on.

 

Reflection Papers:  A few times during the semester you will be given writing assignments to complete.  These papers must be typed.  Their length and content will vary.   These informal papers will be graded mainly on their content and completeness, but you should write in complete sentences and clearly express your thoughts.  Reflection paper will contribute 25 points toward your final grade.

 

Proof Portfolios:  Each class participant will be expected to develop a proof portfolio.  This portfolio will consist of samples of mathematical proofs of key types.  A proof cannot go into your portfolio until it has been rewritten and revised to both of our satisfaction.  At the end of the semester your portfolio will be graded out of 50 points (your grade will be based on how many completed proofs have been added to your portfolio).

 

Exams:  This course will have two unit exams plus a comprehensive final exam.  The final exam will be given from 9:00-11:00am on Wednesday, December 16th.  All exams will be closed book and closed notes.  I will allow the use of an approved calculator (no graphing calculators are allowed).  No other electronic devices (cell-phones, etc.) are allowed.

 

The credit given on exam questions will be proportional to the amount of correct work shown.  Little to no credit will be given if sufficient work is not shown, even when the final answer is correct.  Each in class exam will be worth 100 points.  The final exam is worth 200 points. 

 

Presentations:  As I mentioned above, each of you will be expected to give at least one presentation of a proof during the course.  Developing the ability to communicate mathematical idea to your peers is an important skill.  I recognize that this may cause some anxiety for some of you.  Come talk with me if you are worried about this.

 

Course Grading Policy: Your final grade in the course will be computed as follows:

 

Homework/Quizzes/Activities:               150 points

“Proof Portfolio”                 50 points

Projects:                 50 points

Presentations                 25 points

Reflection Papers                 25 points

Unit Exams:               200 points

Final Exam:               200 points

Total:               700 points

 

Final letter grades will be assigned based on the following scale:

 

96.5-100.0%               A+                              81.5-86.4%               B                               69.0-71.4%               C–

91.5-96.5%               A                               79.0-81.4%               B–                              66.0-68.9%               D+

89.0-91.4%               A–                              76.5-78.9%               C+                              60.0-65.9%               D

86.5-88.9%               B+                              71.5-76.4%               C                              <60.0%                              F

                                                                                         

Make-up Work:  Because you are allowed to drop several scores, I only give make-up assignments for extreme personal emergencies or for absences which are officially sanctioned by the University.  I expect written documentation in either of these cases.  If you miss an exam and a make-up exam is not warranted, you may still replace your grade on one missed exam with your un-scaled percentage score on the final exam.

 

Special Accommodations: Minnesota State University Moorhead is committed to providing equitable access to learning opportunities for all students.  The Disability Resource Center (DRC) is the campus office that collaborates with students who have disabilities to provide and/or arrange reasonable accommodations.   

•        If you have, or think you may have, a disability (e.g. mental health, attentional, learning, chronic health, sensory or physical) please contact the DRC at (218) 477-4318 (V) or (800)627.3529 or 711 (MRS/TTY) to schedule an appointment for an intake.

•        Additional information is available on the DRC website: http://www.mnstate.edu/disability/

•        If you are registered with the DRC and have a current Accommodation Letter, please schedule an appointment to visit with me, during my office hours, to discuss implementation of your accommodations.

 

Academic Honesty: You are expected to do your own work.  You may work with others and get help on assignments, but the work you submit must be your own.  During exams and quizzes you will not be allowed to get help from others.  Cheating and plagiarism will not be tolerated in any course at any level.  See the MSUM Academic Honesty policy for more information on the possible consequences of cheating.

 

Thanks, And Let’s Have A Great Semester!!

 

 

Math 311 – Section 01 Course Page

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