This will be an on-campus class - but the office hours will be remote via Zoom.

           Prof. Ram's Zoom Meeting ID - 722 280 1561.   Waiting Room will be enabled -

           and a Passcode may be sent to your official FIU e-mail later on.

          Contains the name of the textbook, prerequisites for the course, relevant sections of the
          textbook, exam policy, schedule of exams, grading scheme, and other pertinent information.

         Textbook:  Introductory Combinatorics (Fifth Edition) by Richard A. Brualdi (Pearson, 2010)

         Corrections: A pdf file with corrections to Brualdi's Fifth Edition of Introductory Combinatorics


          Homework sheet                           
Contains the list of HW Problems for the course including the assigned supplementary problems.
          You can find answers or hints to most of the assigned problems in the back of the textbook & more
          detailed solutions in the Solutions to Homework Problems below.  

           Supplementary HW Problems    (on the Pigeon Hole Principle & on Difference Equations) 


          Solutions to HW Problems:

           Ch.2&4 (p.1-20)                 Ch.5&6 (p.21-36)                Ch. 3 (p.37-50)       

           Ch.7 (p.51-75)                    Ch.8 (p.76-84) 


         Review Sheets: 

          Most of the questions in the exams usually come from the topics in the Review but this cannot

           always be so because everything we do cannot always fit on one page.

          Review for Test#1                             Review for Test #2

          The Review for the Final just consists of the Reviews for Tests #1 & #2.


          Modified Class notes

                   Ch.0 -  Table of Contents and Preliminaries                                         

                    Ch.1 -  Permutations & Combinations of Sets  (19 pages)

                    Ch.2 -  Combinations & Permutations of Multi-sets  (8 pages)

                    Ch.3 -  The Binomial & Multinomial Coefficients  (15 pages)

                    Ch.4 -  The Inclusions-Exclusion Principle & its applications (18 pages)

                    Ch.5 -  The Pigeon-Hole Principle & its applications (12 pages)

                    Ch.6 -  Recurrence Equations & their applications (18 pages)

                    Ch.7 -  Generating Functions & their applications (15 pages)

                    Ch.8 -  Stirling Numbers & related partition numbers (22 pages)

                    Ch.9 -  Minimal & Elementary Symmetric functions (not included)

                    Ch.10- The Combinatorics of Infinite Sets (not included)                       


           Past Exams: 

            Future exams cannot always be very similar to the past exams because things have to change.

                   Summer 1990 Test #1,                             Summer 1990 Test #2

                   Summer 2000 Test #1,                             Summer 2000 Test #2

                  Summer 2002 Test #1,                             Summer 2002 Test #2

                   Spring 2006 Test #1,                                Spring 2006 Test #2

                  Fall 2014 Test #1,                                    Fall 2014 Test #2

                   Fall 2015 Test #1                                     Fall 2015 Test #2 

                   Fall 2016 Test #1                                     Fall 2016 Test #2 

                   Fall 2017 Test #1                                     Fall 2017 Test #2 

                   Fall 2019 Test #1                                     Fall 2019 Test #2  

                   Fall 2020 Test #1                                     Fall 2020 Test #2    

                   Fall 2021 Test #1                                     Fall 2021 Test #2  


   Learning  Assistant (GTA) (Click on the name for a photo - when available)

             No LA (Learning Assistant) or TA (Teaching Assistant) were available for this course.


            Times:    N/A

            Location:  N/A



             Tutoring services:     

             You can also get help in Mathematics from the FIU Centre for Academic Success, GL 120,  MMC.

             You can make appointments by calling 305- 348-2441 (MMC).    For more information check out the link below