Northwestern University
EECS 203: Introduction to Computer Engineering
Spring 2015
Homework 1
Note: Problems worth zero points are for practice. They will be ungraded you dont have to hand them in. Do
however, make sure that you know how to solve them.
1.

Northwestern University
EECS 203: Introduction to Computer Engineering
Spring 2015
Homework 3
Note: Problems worth zero points are for practice. They will be ungraded you dont have to hand them in. Do
however, make sure that you know how to solve them.
1.

EECS 212
Mathematical Foundations of
Computer Science
Lecture 15: Deviations from Mean
Announcements
1. Midterm on October 28th (Friday) in class.
2. You will be allowed one regular sheet (A4/ letter) of paper
to write down formulae etc.
3. Any student wi

EECS 212
Mathematical Foundations of
Computer Science
Lecture 11: Probability Basics
Announcements
1. PS3 due Wednesday 3pm, October 19th.
2. PS4 due Wednesday 3pm, October 26th.
3. Midterm in class on Friday, October 28th.
4. Questions regarding grades s

EECS 212
Mathematical Foundations of
Computer Science
Lecture 10: Binomial Theorem contd.,
Probability
Announcements
1. PS3 due Wednesday 3pm, October 19th.
2. Midterm on October 26th (Wednesday) in class.
3. There will be class the Wednesday before Thank

EECS 212
Mathematical Foundations of
Computer Science
Lecture 16: Trees, Connectivity &
more
Announcements
1. Midterm grades will be out this week.
2. Next assignment is out: due before class on Wednesday,
November 9th.
Recap: Simple Graphs
G(V,E) is a si

EECS 212
Mathematical Foundations of
Computer Science
Lecture 5: Sets, Mappings,
Asymptotics
Announcements
1. PS1 is out. Due Monday 3pm, October 3rd.
2. Check out the Syllabus page for lecture slides and
references.
Outline
Induction & Recurrences
Basi

EECS 212
Mathematical Foundations of
Computer Science
Lecture 25: Number Theory
Announcements
1. Next assignment due before class on Wednesday,
November 23rd.
2. Final exam in-class portion on Dec 5th (23 points)
3. Take home final carries 10 points (will

EECS 212
Mathematical Foundations of
Computer Science
Lecture 12: Union Bound, Birthday
Paradox
Announcements
1. PS3 due Wednesday 3pm, October 19th.
2. Midterm on October 28rd (Friday) in class.
Back to Sets and Sum Rule
Sum Rule Revisited
Probability: I

EECS 212
Mathematical Foundations of
Computer Science
Lecture 22: Matrices, Linear Algebra
Announcements
1. Next assignment due before class on Wednesday,
November 16th.
Matrix Algebra and Graphs
Adjacency Matrices
Graph G with n vertices.
The adjacency m

EECS 212
Mathematical Foundations of
Computer Science
Lecture 24: Linear Programming,
LP Duality
Announcements
1. Next assignment due before class on Wednesday,
November 23rd.
2. Can solve all problems after this class.
Linear Programming
Optimization
Sup

EECS 212
Mathematical Foundations of
Computer Science
Lecture 6: Mapping, Functions,
Growth of Functions
Announcements
1. PS2 is out. Due Wednesday 3pm, October 12th.
2. Check out the Syllabus page for lecture slides and
references.
Mappings, Functions
Ma

EECS 212
Mathematical Foundations of
Computer Science
Lecture 8: Permutations,
Combinations & Binomial Theorem
Announcements
1. PS2 due Wednesday 3pm, October 12th.
2. Go to the recitation for solutions to PS1.
3. New poll on Piazza to figure out if there

EECS 212
Mathematical Foundations of
Computer Science
Lecture 26: Number Theory &
Cryptography
Announcements
1. Next assignment due on Wednesday, November 30th.
2. Can solve all problems after this class.
3. Recitation today (5pm 6pm)@Tech L160.
4. Office

Number Theory
GCD and its properties
| means n is a multiple of k.
Even numbers: 2 ; Odd numbers: 2 1
gcd(, ): largest common divisor between and
gcd(, ) is smallest +ve integer combination of , (Thm)
Every common divisor of , divides gcd(, )
gcd , =

EECS 212
Mathematical Foundations of
Computer Science
Lecture 14: Great Expectations,
Deviations
Announcements
1. Midterm on October 28th (Friday) in class.
2. You will be allowed one regular sheet (A4/ letter) of paper
to write down formulae etc.
3. Any

EECS 212
Mathematical Foundations of
Computer Science
Lecture 13: Random Variables
Announcements
1. PS4 due Wednesday 3pm, October 26st.
2. Midterm on October 28th (Friday) in class.
3. You will be allowed one regular sheet (A4/ letter) of paper
to write

EECS 212
Mathematical Foundations of
Computer Science
Lecture 21: Matchings,
Planar graphs
Announcements
1. Next assignment due before class on Wednesday,
November 16th.
2. Lectures will be given by Prof. Anindya De on Monday and
Wednesday.
Perfect Matchi

EECS 212
Mathematical Foundations of
Computer Science
Lecture 7: Asymptotics, Counting
Announcements
1. PS2 is out. Due Wednesday 3pm, October 12th.
2. Check out the Syllabus page for lecture slides and
references.
Limits and Big-Oh
lim
()
()
lim
=0

EECS 212
Mathematical Foundations of
Computer Science
Lecture 19: Spanning Trees, Graph
Coloring
Announcements
1. Next assignment due before class on Wednesday,
November 9th.
Spanning Trees
A spanning tree of a graph G is a tree that touches every node
of

EECS 212
Mathematical Foundations of
Computer Science
Lecture 20: Bipartite Graphs,
Matchings
Announcements
1. Next assignment (PS6) due before class on Wednesday,
November 19th.
2. PS5 deadline extended till noon tomorrow.
3. Community dialogue today i.e

EECS 212
Mathematical Foundations of
Computer Science
Lecture 27: Public-Key
Cryptography, Groups
Announcements
1. Next (last) assignment due on Wednesday, November
30th.
2. Final exam in-class portion on Dec 5th (in class).
3. Final exam take home will b

EECS 212
Mathematical Foundations of
Computer Science
Lecture 9: Binomial Theorem,
Probability
Announcements
1. PS2 due Wednesday 3pm, October 12th.
2. The midterm is on Wednesday, October 26th.
3. Register on Piazza if you havent done it already:
http:/p

EECS 212
Mathematical Foundations of
Computer Science
Lecture 18: Spanning Trees,
Connectivity & more
Announcements
1. Next assignment due before class on Wednesday,
November 9th.
2. Mid-term scores will be out tonight/ tomorrow. You can
pick up the grade

EECS 212
Mathematical Foundations of
Computer Science
Lecture 21: Linear Programming
Announcements
1. Next assignment due before class on Wednesday,
November 23rd.
Refresher: Eigenvalues,
Eigenvectors
Given any matrix , is an eigenvector iff
for some scal

EECS 212
Mathematical Foundations of
Computer Science
Lecture 16: Graph Theory, Networks
Announcements
1. No assignment this week.
2. Next assignment which will be given tomorrow (November
1st ), due on November 9th Wednesday.
Networks
Partial Map of the