Course:  MCS 421,  Combinatorics
</br>
CRN: 34232 and 34233</br>

Time: MWF 11:00-11:50am
</br>
Place: 204 Taft Hall 
</br>

<p>Professor: Dhruv Mubayi
</br>
Office:  620 SEO
</br>
E-mail: mubayi@uic.edu
</br>
Course Web Page: http://www.math.uic.edu/~mubayi/421/Spring25/421Spring25info.html</br>

Office Hours: TBD      <p>
      
      
<p>Grading Policies:</br>

Attendance and class participation: 15%</br>

Homework (Due Friday every two weeks): 15%</br>

      Three in-class midterms, 35% each (I will drop the lowest): 70%</br>

<br>

      All tests  will be IN PERSON, IN CLASS
<br>
<br>
      Homework will be posted on BLACKBOARD. It must be turned in to BLACKBOARD 
       as a (scanned or typed) pdf file before class starts on the day it is due.
 No late homework will be accepted. You can discuss homework with each other but must write it up
independently with no help from anyone else. Do not search the web for solutions, but you are permitted to search the
web for definitions (or just email me). <br>

       
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<p>  Face Masks: Masks covering both the mouth and nose must be worn at all times by all students, faculty, and 
staff while on campus and inside any building regardless of vaccination status.  If you do not wear a mask, you will 
be asked to leave the classroom and will not be allowed back in class unless or until you wear a mask. If you have 
forgotten your mask, you may pick one up from one of the student information desks on campus during the first two 
weeks of campus. Students who do not comply with the mask-wearing policy will be reported to the Dean of Students.
 Eating and drinking are not allowed in classrooms.   
-->

<p> Accommodations: Disability Policy - Students with disabilities who require accommodations for access and
participation in this course must be registered with the Office of Disability Services (ODS). Please contact ODS a
312/413/-2183 (voice) or 312/413-0123 (TTY).



<p>Prerequisite: GRADE OF C OR BETTER IN MATH 215;
            AND MATH 310 OR 320 OR 330.




<br>
<br>

Course Goals and Learning Objectives: To gain proficiency in the enumeration of discrete structures. <br>



<p> Optional Text: Brualdi, Introductory Combinatorics,
Prentice Hall (any edition).  The text is not required; class notes will suffice for everything. But the text has many extra problems 
(and more details of various math concepts) that you can do for practice.  




<p>Description:
The pigeonhole principle, permutations and combinations, generating permutations and combinations, binomial coefficients, inclusion-exclusion principle, recurrence relations and generating functions, special counting sequences, Polya theory of counting.

  We will attempt to cover most of
Chapters 1--8, 10, and 14 from the text. 

  <br>


<br> Policy for missed or late work, including acceptance of revised work: Homework turned in late will not be graded
unless prior approval of the instructor has been obtained. <br>
<br>

Attendance/Participation Policy: Attendance is required and students are expected to actively participate and engage
with the material during lectures.
 <br>

<br> Community Agreement/Classroom Conduct Policy: Community Agreement: Ground Rules for a Safe/Brave Space 
<ul> <li> Be
present (turn off cell phones and remove yourself from other distractions)</li> 
<li> Be respectful </li> 
<li> Assume good will </li>
<li> Challenge with care - approach discussion as a &quot;think out loud&quot; </li>
<li> Take space/make space </li> 
<li> Try not to make assumptions, seek to understand, not to judge </li> 
<li> Be open to challenges as an opportunity to learn
something new </li> 
<li> Be open to different perspectives 
 Debate the concepts not the person </li>
<li> Be flexible when things don&apos;t
work </li> 
<li> Share helpful tips </li> 
<li>Use preferred names and gender pronouns </li>
<li> No side conversations </li>
<li> Be willing to work
together </li>
  </ul>


<p>
Homeworks are from Brualdi, 5th edition, though I will provide the problems on blackboard, so you do not need the book
<br>

<br> Homework 1, Due Friday January 31:<br>
Chapter 1: 1, 2, 3, 25, 38, 43 <br>

<a href="../spring09hw1sol.pdf"> Solutions</a> to HW1 </br>

<br>

Homework 2, Due Friday February 14 (its somewhat long so start early) <br>
Chapter 2: 1,2,5 a,b, 8,11,16,28 a, 38, 39 a,c, 42, 45 a,b<br>

Chapter 3: 1, 2, 4, 5, 8, 22, 27<br>

<a href="../hw2sol.pdf"> Solutions</a> to HW2 </br>

<br>
TEST 1, Wednesday February 26
<br>
<br>

Homework 3, Due Friday February 28:<br>
Chapter 4: 5, 8a, 20, 35, 37, 47, <br>

Chapter 5: 11, 16, 18, 25, 48, 49<br>

<a href="../hw3sol.pdf">Solutions</a> to HW3 </br>

<br>

Homework 4, Due Friday March 14:<br>
Chapter 6: 2, 5, 6, 7, 10, 13, 19, 22, 23, 26 <br>

<a href="../spring09hw4sol.pdf"> Solutions</a> to HW4 </br>

<br>
TEST 2, Friday April 4
<br>
<br>

Homework 5, Due Friday April 4:<br>
Chapter 7: 1 (all parts), 5, 8, 9, 16, 17, 21, 26, 33, 34, 42, 47 <br> 

<a href="../spring09hw5sol.pdf"> Solutions</a> to HW5 </br>




<br>
Homework 6, Due Friday April 18  <br>
Chapter 8: 1, 2, 9, 12, 19, 25, 26d<br>

Chapter 10: 19, 26, 28, 32, 38<br>


<a href="../spring09hw6sol.pdf"> Solutions</a> to HW6  </br>


<br> Homework 7, Due Friday May 2 <br>
Chapter 10: 42 <br>

Chapter 14: 7, 8, 12, 13d, 15, 19, 26, 35, 48 <br>


<a href="../spring09hw7sol.pdf"> Solutions</a> to HW7 </br>

<br>
TEST 3, Friday May 2
<br>
<br>