MCS 256 Exams

There will be four unit exams and one comprehensive final examination. Some or all of the unit exams may be take-home examinations due on the class day following the day it is given out (due on Monday if given on Friday; due on Thursday if given on Tuesday).

Exam schedule

Date	Exam	Topics
Fri., Feb. 23	1	Recurrences Sums
Tue., Mar. 13	2	Asymptotics Number theory
Tue., Apr. 10	3	Binomial coefficients Enumerative combinatorics
Fri., May 4	4	Generating functions Recurrence relations
Tue., May 22 3:30-5:30	Final exam	Discrete probability Comprehensive

Exam 5: Final Examination

What it will cover

What you need to know
- Discrete probability
- Highlights from the rest of the course: sums, recurrences/induction, asymptotics, binomial coefficientology, combinatorics, and generating functions
Exam procedure

Exam 4

What it will cover
Exam 4 will consist of problems and questions concerning
- generating functions
- recurrence relations
corresponding to the material we have covered in class, in problem assignments, and in chapters 5, 6, and 7 of Graham, Knuth, and Patashnik's Concrete Mathematics. See the calendar for specific sections and page numbers in the text. You are, of course, responsible for the additional material covered in class.

What you need to know
- Generating functions
  - The 1-1 correspondence between sequences and (ordinary) generating functions
  - The most important power series/Taylor series
    - Binomial series, including 1/(1-rz)^m, a typical partial fraction
    - Geometric series
    - Exponential power series
  - Basic maneuvers: the connections between basic operations on generating functions and their sequences and vice versa
  - How to find the generating function of the sequence satisfying a given recurrence relation
  - Partial fractions
    The MAIN THEOREMS: pp. 341-342
  - Exponential generating functions
- Solving recurrence relations
  - Homogeneous linear recurrence relations with constant coefficients
  - Nonhomogeneous linear recurrence relations with constant coefficients
  - Simple divide-and-conquer recurrence relations

Exam procedure
Exams will be available Friday, May 4, at my office, Olin 307. Fill in the information on the exam sign-out sheet there. You will have two hours to complete the exam entirely on your own, using only the CONCRETE MATHEMATICS text and your notes, and return it to Olin 307. You must in any case finish and return exam before 8:00 a.m. Monday, May 7.

Exam 4 instruction page (postscript) (pdf)

Exam 3

What it will cover
Exam 3 will consist of problems and questions concerning
- binomial coefficientology
- enumerative combinatorics
corresponding to the material we have covered in class, in problem assignments, and in chapter 5 of Graham, Knuth, and Patashnik's Concrete Mathematics. See the calendar for specific sections and page numbers in the text. You are, of course, responsible for the additional material covered in class.

What you need to know:
- Binomial coefficientology
  - The definition of binomial coefficient
  - The top ten binomial coefficient identities (p. 174)
  - High order differences
    - The Newton series (also called the Newton advancing difference formula)
    - Formula (5.40) for the n^th difference
      and its applications, including the formulas at the bottom of page 189 and (5.42)
  - Binomial inversion (p. 192)
- Enumerative combinatorics
Exam procedure
Exam 3 will have two parts.
The first and main part of the exam will be available Tuesday, April 10, at my office, Olin 307. For this part of the exam you may use your notes, the textbook (but not other texts), and a calculator (but not a computer or calculator algebra system). Fill in the information on the exam sign-out sheet when you pick up your exam. You will have two hours to complete the exam. Return it immediately to Olin 307. All exams must be completed by 8:00 a.m. Thursday, April 12.
The second part will be given in class on Thursday, April 12. It will take about half the period and will have a time limit. It will test your knowledge of basic definitions, key formulas, and counting methods. For this part of the exam you will not be able to use any notes, texts, or calculators.

Exam 3a instruction page (postscript) (pdf)

Exam 2

What it will cover
Exam 1 will consist of problems and questions concerning
- asymptotics
- integer functions
- number theory
corresponding to the material we have covered in class, in problem assignments, and in chapters 9, 3, and 4 of Graham, Knuth, and Patashnik's Concrete Mathematics. See the calendar for specific sections and page numbers in the text. You are, of course, responsible for the additional material covered in class.

What you need to know: (postscript) (pdf) (html)

Exam procedure
Exam 2 will have two parts. The first part will be administered in class on Tuesday, March 13, and will cover basic definitions and algorithms. For this part of the exam you will not be able to use any notes, texts, or calculators. It will take about 20 minutes, and will be started after a review session at the beginning of class. The second part of the exam will be available Tuesday, March 13, at my office, Olin 307. For this part of the exam you may use your notes, the textbook (but not other texts), and a calculator (but not a computer or calculator algebra system). Fill in the information on the exam sign-out sheet when you pick up your exam. You will have two hours to complete the exam. Return it immediately to Olin 307. All exams must be completed by 8:00 a.m. Thursday, March 15.

Exam 2b instruction page (ps) (pdf)

Exam 1

What it will cover
Exam 1 will consist of problems and questions concerning
- Recurrence relations
- Induction proofs
- Summation
corresponding to the material we have covered in class, in problem assignments, and in chapters 1 and 2 of Graham, Knuth, and Patashnik's Concrete Mathematics.
UNIT 1 tactics, techniques & tricks

Exam procedure
Exams will be available Friday, February 23, at my office, Olin 307. Fill in the information on the exam sign-out sheet there. You will have two hours to complete the exam entirely on your own and return it to Olin 307. You must in any case finish and return exam before 8:00 a.m. Monday, February 26.

Exam 1 instruction page (Postscript) (HTML)

Make-up policy

Make-up exams will not be given except for medical or family emergency reasons. Students who will be absent from an exam for a school-sponsored event should arrange with me in advance to have an exam sent along with the coach. If you miss a class for any reason, you are still responsible for learning what was covered in class and for getting any homework that is due turned in on time. If there is a compelling reason for granting an extension, you must negotiate the arrangements with me.