Discrete Mathematics Math
210 Syllabus
Fall 2017
Instructor: Margaret Menzin
Emails: menzin@simmons.edu (preferred)
Office: S209 (2nd floor of the Science Center)
Phones: x2704 at Simmons (617-521-2704)
781-862-5107 at home. Please do not call after 10 p.m. except for emergencies.
Office Hours: I am here MWF from
9:00-11:00 (usually from 7:15-8:00) and
Mon 12:30 - 2:00 and 3:20 on
Wed sometimes 2:00-3:00
Fri all day.
Please give me a heads up if you plan to come during lunch. For other times please send me an email ahead of time as some
meetings have sporadic schedules.
Note: There is no class on Friday
Sept. 22, 2017
This meeting will be made up at a
time to be determined by us.
Accommodations
for Special Needs:
Reasonable accommodations
will be provided for students with documented physical, sensory, systemic,
cognitive, learning, and psychiatric disabilities. If you have a disability and
anticipate that you will need a reasonable accommodation in this class, it is
important that you contact the Academic Support Center Director at 617-521-2471
early in the semester. Students with disabilities receiving accommodations are
also encouraged to contact their instructors within the first 2 sessions of the
semester to discuss their individual needs for accommodations.
Title IX and the Simmons College Gender‐Based Misconduct Policy
Title IX Federal law states that all students have the right to gain an education free of gender‐based discrimination.
Some examples of gender-based discrimination, as defined by this law include
sexual harassment or exploitation,
sexual assault, domestic/dating violence, and stalking.
In compliance with Title IX, Simmons College has a ‘Gender-Based
Misconduct Policy’ which defines these forms of misconduct, outlines College protocol and procedures for
investigating and addressing incidences of gender-based
discrimination, highlights interim safety measures, and identifies on and off-campus
resouces. The policy and a list of resources is located here:
https://internal.simmons.edu/students/general‐information/title‐ix/gender‐based‐misconduct‐policy‐for‐
students‐faculty‐staff‐and‐visitors. Additionally, the Gender-Based
Misconduct Policy has a Consensual Relationships clause that prohibits intimate, romantic or sexual relationships between students, faculty, staff,
contract employees of the College, teacher’s assistants, and supervisors at internship/field placement sites.
Text:
Epp - Discrete
Mathematics and Its Applications – 4th
edition. McGraw Hill.
Please note
that there should be plenty of used copies available!
Accommodations for Special
Needs:
Reasonable
accommodations will be provided for students with documented physical, sensory, systemic,
cognitive, learning, and psychiatric disabilities.
If you have a documented disability and anticipate needing accommodations in this course,
it is your responsibility to register with the Disability Services office as soon as possible to
ensure that requested accommodations may be implemented in a timely fashion.
For more information or to request academic accommodations, contact the Disability Services Office
located in Room E-108 of the Main College Building. They are available by phone at 617-521-2474 or you may
email Tim Rogers at timothy.Rogers@simmons.edu.
Students with disabilities receiving accommodations are also encouraged to
contact their instructors within the first 2 sessions of the
semester to discuss their individual needs for accommodations.
Approach
to
the Course:
This
course has two major goals: to learn certain material
fundamental to mathematics and computer science, and to
increase your
sophistication and ability in handling abstract problems.
In order to achieve these goals you will be very 'hands on' through out the
course; you will spend a lot of time talking about and writing about
mathematics. That is, this is essentially a flipped course and definitely a course
with a lot of small group work and
much less lecturing than most math courses.
This means that the course is a lot of fun (especially since the material itself is a lot of
fun) . It also means that it is critical that you do the assigned
reading and problems before class and are well prepared for class. Remember
that your entire group is depending on you!
In order to help you stay motivated about getting the reading done on time
there will be pop quizzes on the reading material. The total of your grades on the pop quizzes count
as one hour exam.
I also expect you to stay current on the VoiceThreads and to answer the questions posed in them.
Some
strategies for success in this course:
Reading
mathematics
is sometimes slow going, and a section will usually
require two or three readings.
It is a good idea to read the section first for the general flow
of ideas,
skipping over anything that doesn't seem obvious.
On the second and third readings, now that you know where the
book is heading,
you should read the book closely, making note of anything that
does not make
sense, or any calculation you can't follow.
As
you re-read, you may also choose to make a note to
yourself to ask about something in class. For example, 'p.
37, line 4
doesn´t make sense' is a fine thing to ask about in the
beginning of class (and
a lot more helpful than I'm lost'.) I also strongly encourage you to email me the evening before class
with the same kind of reference to unclear items.
I encourage you to email me and ask questions in class; it is rarely the case
that only one student finds something mysterious. If I do not ask for
questions at the beginning of class, and you have some, please ask your
questions.
All
assignments will be posted in Moodle. Most of the problems are from your text, a few will be from handouts. In each
assignment you are expected to read carefully the section of the
book from which the problems are assigned. There will also be
some relatively routine problems to do and
there may be a video to watch.
In class we will be doing more challenging problems which will deepen your understanding of the material.
Although we may not have time to discuss all the material in
class, you are responsible for everything in those sections unless
explicitly told
otherwise. Indeed, because the aim of the course is to
increase your
sophistication, as the course progresses you will be asked to
'dig out' more of
the material on your own.
Our class time will be spent on working more difficult problems
in groups or
individually. In
other words my aim is
to “flip” the course, and to lecture as little as possible.
Talking
about mathematics:
A lot of class
time will be used to work on problems in small groups.
These problems
will be similar to those due for homework. In order to
contribute to your
group you must read the material and try some of
these problems
before coming to class. The purpose of the small group
work is to get you
to talk about mathematics as a way to master it and to help you
develop strategies
for problem solving.
Writing
about mathematics: Understanding
mathematics
also means being able to write about it. This course is 'writing
intensive' and I am very excited about the
emphasis on writing
in this course. Just as the small group work entails a lot
of talking
about math as a way to understand it, the assignments also
require a lot of
writing about math as a way to understand it. So you will
find many small
assignments - writing proofs and problem solutions. Some
writing assignments
will be handed in; others will be peer evaluated.
Grading:
There
will be a test or other summative effort at the
end of Units 1, 2, and 3. a final. ( Unit 4 is on the final) There will also be
pop quizzes. Each of
the tests, the final, and
the sum of the pop quizzes will count equally.
The Course – Outline of the Material
In the first part of the course we examine Aristotelian or truth table logic and its application to the design of logic circuits for computers. Importantly, we learn to be precise about our language, and see how that helps us to state our ideas clearly and unambiguously. This also leads us to understand different ways we can prove theorems, and to practice constructing proofs (something we will do a lot of).
Truth table logic is equivalent to certain simple circuits - series and parallel circuits to implement 'and' and 'or' gates in computers. We will examine these correspondences. see the design of circuits for functions such as addition in a computer./p>
Quantified logic introduces the phrases 'for all' and 'there exists'. You will translate English, database,and mathematical statements into this format , and learn how to negate quantified statements. In this context we will discuss the difference between and an example and a proof. We will apply our knowledge to writing focused queries for Internet searches and for databases.
We will learn in
In this unit we learn how to use one of the most important proof techniques of mathematics- namely, mathematical induction.
Mathematical induction also has an important relationship to recursion, a basic programming technique. We will examine some of the issues in recurrence relations, but not all of Chapter 5.
We also look more deeply at set theory and come to understand the connections among propositional logic, set theory, and the logic gates which are used to build circuits in computers. This examination leads to the consideration of what it means for a system to be complete,
consistent and decidable, as propositional logic is. Quantified logic does not have the
neat characteristics (complete, decidable) of truth table logic. We revisit
these notions and learn about Russell's paradox, Godel's
Incompleteness Theorem
(a fundamental result in the foundations of mathematics) and about
the Halting
Problem and about the famous question 'P=NP?' (the
fundamental outstanding problem in foundations of computer
science).
Finally, a return to the subject of functions (including one to one, onto, and inverse functions)
prepares us for the topic of cardinality (size) of sets.
Mathematicians, in
addition to
worrying about what it means to prove something and how to prove
things, also
spend a lot of time (in both this unit and the next) thinking about measuring things.
We will discuss what it means for two sets to have
the same number of elements ( or cardinality). For
example, we will ask if all infinite sets are the same size.
In addition to measuring sets, we will
also try to measure how hard a problem (such as factor an integer
into primes)
is, or the complexity of the algorithm to solve it. This has applications to cryptography, since you would
like breaking a secret code to be as hard as possible.
We will see how hard problems are
valuable to people trying to protect computer systems from
hackers.
Unit 3 - Counting Up a Storm (Chapter 9)
Here we study basic ways
of counting:
the pigeon-hole principle, the law of inclusion-exclusion, the
binomial theorem
(and Pascal's triangle), counting permutations and combinations,
and some
discrete probability. The relationships of probability to
set theory and
measurement tie this to Units 1 and 2 of the course. A
substantial amount
of effort is expended on leaning how to analyze these problems.
Unit 4 – Graphs and Trees (Chapter 10)
The basic notions of graph theory are introduced - vertices, edges, degree of a vertex, connected components, directed and undirected graphs, and acyclic graphs or trees.
As time allow, a variety of graph theory problems and their solutions will be explored -Eulerian and Hamiltonian graphs, graph isomorphism, graph coloring, minimal spanning trees, etc. - as well as the representation of graphs in computers and their applications to real world problems.