MATH 101 PROBLEM SESSION #1
Section 1.1/Section 1.2
How can you tell if two terms are like terms?
What does it mean to simplify an algebraic expression?
Section 1.3
1. True or False: If a point is on the y-axis, its x-coordinate is 0.
2. True or False: Th
MATH 101 PROBLEM SESSION #5
Section 4.1
1.
When graphing the solutions of an inequality, what does a parenthesis signify? What does a bracket signify?
2.
Solve, write your answer in interval notation and then graph:
(a)
9(4x 1) < 3(2x + 2)
(b)
12y + 6 < 9
MATH 101 PROBLEM SESSION #2
Section 2.1
1. Explain in your own words what a function is.
2. Determine whether (2, 3), (2, 4) and (2, 5) is a function.
3. Determine whether (0, 3), (1, 3) and (2, 3) is a function.
4. If P(x) = x2 5x, is P(2) + P(3) = P(2 +
MATH 101 PROBLEM SESSION #2
Section 2.1
1. A function is a relation from a set, called the domain, to another set, called the range, such that each element
in the domain corresponds to exactly one element in the range.
2. The relation cfw_(2, 3), (2, 4),
MATH 101 PROBLEM SESSION #4
Section 3.1
1. When is it easier to use the addition method to solve a system? When is it easier to use the substitution method?
2. When using the addition method to solve a system, how can you tell if the system (a) has no sol
MATH 101 PROBLEM SESSION #1
Section 1.1/Section 1.2
How can you tell if two terms are like terms?
What does it mean to simplify an algebraic expression?
Section 1.3
1. True or False: If a point is on the y-axis, its x-coordinate is 0.
2. True or False: Th
Discrete Structures, CSCI-150.
Information
Information
Propositions
Operators
Fighting Complexity
Equivalence
Please use the Blackboard page for reference.
Course sections, instructors
Course Description
Assessment
Homework Policies
Assignments Tab
p
Predicates and Quantiers.
Predicates
Predicates
Quantiers
Scope, bound
variables
Propositional logic, studied previously, cannot adequately express
the meaning of all statements in mathematics and in natural language.
Nested quantiers
Distributivity
Negat
Fibonacci Numbers.
Solving Linear Recurrences
So, whats with the Rabbits?
Introduction:
Fibonacci Numbers
Take a pair of rabbits that take one month to become mature. When
a pair is mature, it it produces a new pair each month. Each new
pair takes one mon
Binary Search Example
1
5-2
32
48
64
Binary Search Example
1
5-3
Is x > 32?
32
48
64
Binary Search Example
1
5-4
Is x > 32?
32
Answer: Yes
48
64
Binary Search Example
1
5-5
Is x > 32?
Is x > 48?
32
Answer: Yes
48
64
Binary Search Example
1
5-6
Is x > 32?
MATH 101 PROBLEM SESSION #6
Section 5.1
1. What is a polynomial function?
2. What do we mean when we describe the graph of a polynomial function as smooth and continuous?
3. Explain how to determine the leading coefficient of a polynomial.
4. Explain how
MATH 101 PROBLEM SESSION #10
Section 7.2
1
1. Explain how you would decided whether a n is a real number.
2
2. The fraction
1
2
1
is equal to . Is 16 4 equals to 16 2 ? Explain.
4
2
1
3. How would you evaluate an expression with a mixed-number exponent? F
MATH 101 PROBLEM SESSION #4
Section 3.1
1. When is it easier to use the addition method to solve a system? When is it easier to use the substitution method?
2. When using the addition method to solve a system, how can you tell if the system (a) has no sol
MATH 101 PROBLEM SESSION #3
Section 2.4
1. If you were given the standard form of an equation, explain how to find the x-intercept; the y-intercept?
2. The graph of a linear equation has no points in Quadrants I and II. What must the slope of this line be
1.1 Interval Notation
1.5 Problem Solving and using Formula
Mystery Number
1) A T.V is on sale for 80% of the original price. It cost's $400 on sale. What is the original
price ?
2) A coat is on sale for 20% o the original price. The sel
"-00 T-Mobile LTE
< Inbox (3)
12:11 PM
cfw_E 1 IF 3396:]-
AV
IUUEI? EI'L II-OEI- HM
Early College Initiative at Hunter College
Student Class Schedule
Kyoroh Soinvr'lus
TUESDMr VI'EDI-IESDiIh'r THURSDAY FRIDMr
Open
Recreation
HS G
MATH 101 PROBLEM SESSION #7
Section 5.5
1. Explain why a perfect square trinomial cannot have a negative last term.
2. If you have the choice of factoring a polynomial as the difference of two squares or as the difference of two cubes,
which do you do fir
MATH 101 PROBLEM SESSION #8
Section 6.1
3b a
a 3b
to an answer of
. Are the two answers the same?
2b a
a 2b
2. In which parts can you divide out the 4s?
4x 4 y
4x 4 y
4x
4 x
4x
b.
c.
d.
e.
a.
4 4y
4 y
x4
4a 4b
4z
1. A student compares an answer of
3. Sinc
MATH 101 PROBLEM SESSION #9
Section 6.6
1
1
and 5x = 9x are equivalent equations and give a reason for your decision.
5x 9 x
1
1
(b)
Can we just multiply both sides of
by the LCD?
5x 9 x
2. Explain why is it necessary to check the solutions of a rational
Discrete Mathematics for Computer Scientists
Big O Notation
Big O Denition
Denition
Given two functions f : R R and g : R R, we say that
f = O(g) if there are positive numbers no and c such that
f(x)
for every x
c g(x)
n0 .
Write using the standard notati
Recursion Trees.
Computational Growth
Example: binary search
Divide and Conquer
Algorithms
Merge sort
Recursion Trees
Order of Growth
Time Complexity
Oliev has chosen a number x between 1 and n (Oliev is a computer).
We are allowed to ask Oliev only two t
Conditioning
Tree diagrams
Bayes Formula
Discrete Mathematics for Computer Scientists
Conditional Probability and Independence
c 2015 by Felisa J. Vzquez-Abad
Independence
Conditioning
Tree diagrams
Bayes Formula
Independence
Previously, on CSCI 150.
Samp
Renaissance
Statistical Theory
Statistics Timeline
Discrete Mathematics for Computer Scientists
Brief History of Statistics
c 2010 by Felisa J. Vzquez-Abad
Renaissance
Statistical Theory
Statistics Timeline
Renaissance
Venice and Florence. XV Century: Gre
Pigeonhole Principle.
Bijection. Inclusion-Exclusion.
Double Counting
A typical situation
The Pigeonhole
Principle
Inclusion-Exclusion
BIjection
Double Counting
A drawer in a dark room contains red socks, green socks, and blue
socks. How many socks must y
Random Variables
Bernoulli
Independent Trials Process
Bernoulli Trials
Binomial
Discrete Mathematics for Computer Scientists
Probability Theory
Random Variables and Processes
c
2014
by Felisa J. Vzquez-Abad
Geometric
Random Variables
Bernoulli
Independent
Sets. Ordered pairs.
Sets
Sets
Ordered pair
Relations
Equivalence Relation
The set theory is a branch of mathematical logic
that was created by Georg Cantor in 1870s.
Functions
Bijection
Def. A set is a unordered collection of objects being
regarded as a
Expectation
Linearity
Variance
Independence
Binomial Distribtuion
Geometric Distribution
Conditional Expectation
Discrete Mathematics for Computer Scientists
Probability Theory
Expectation
c 2014 by Felisa J. Vzquez-Abad
a
Expectation
Linearity
Variance
I