SUFFOLK COUNTY COMMUNITY COLLEGE
LETTER-OF-INTENT
T0 COLLEGE ASSOCIATE DEAN FOR
CURRICULUM DEVELOPMENT
PROPOSER E-MAILS LETTER-OF-INTENT AS WORD DOCUMENT TO DR.
ALLEN JACOBS, COLLEGE ASSOCIATE DEAN FOR CURRICULUM
DEVELOPMENT. Dr. Jacobs determines which campuses are affected by proposal
and fills out the Response to Proposal Form below. Dr. Jacobs returns the Letter-of
Intent and Response to Proposal forms to proposer with copies to the appropriate
Executive Deans.
Proposer___Elizabeth Chu__________ Campus:
(name)
A_ X___
E____
G_____
Department/Discipline__Mathematics and Computer Science_________________
Telephone___4271______________________ E-mail_chue@sunysuffolk.edu_
Name of Curriculum/Course Proposal___ MAT200 – Language, Logic, and Proof
Date________________________________________________________
College Associate Dean for Curriculum Development completes form below this line.
******************************************************************
Type of Proposal
Course
New________XX_______________________
Revised_______________________________
Adoption______________________________
Curriculum
New__________________________
Revised________________________
Expedited Revision_______________
A.A._____ A.S. _____ A.A.S _____
Certificate __
This proposal requires the following approval(s)
Single Campus _ X____
*College_____
*College approval is required when the proposal has an
impact on more than one campus.
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 2
SUFFOLK COUNTY COMMUNITY COLLEGE
LETTER-OF-INTENT
T0 COLLEGE ASSOCIATE DEAN FOR
CURRICULUM DEVELOPMENT
Description of proposal idea and rationale.
(Proposer should present description of proposal idea on this page along with a
rationale for the proposal.)
With the recent program review of the Mathematics Emphasis program
Liberal Arts and Sciences: Mathematics Emphasis Ammerman / LAMA-AA
(102-1) Hegis Code –5649, one of the recommendations is to create a
proofs course. This course will be numbered MAT200 and the title will be
Language, Logic, and Proof.
This will be a basic course in the logic of mathematics, the construction of
proofs and writing proofs. The mathematical content is primarily set theory,
logic, number theory, introduction to some basic concepts related to
functions and relations, and some Euclidean Geometry. There is considerable
focus on writing proofs. This course is designed to better prepare students to
take higher level mathematics courses.
The learning outcomes are:
Upon successful completion of this course, the student will able to:
A. use logical language, operations, and rules to create and
interpret mathematical proofs.
B. use the definition of sets and maps between them to create and
interpret proofs about sets.
C. use concepts from number theory and elementary Euclidean
geometry to create and interpret proofs from those topics.
D. prove elementary facts about functions and relations.
E. read and critique proofs, and recognize basic errors in reasoning.
F. construct and write mathematical proofs by using methods, such
as; mathematical induction, proof by contradiction, direct proof,
and proof by contraposition.
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 3
Rationale:
Many of our peer institutions have a proofs course in their curriculum. Also,
many of the four year colleges’ curricula have an introductory proofs course
in the first two years. In order to better prepare our students to seamlessly
transfer to a four-year college, the Program Review Committee
recommended to create a proofs course. It will be numbered MAT200 and
title will be Language, Logic, and Proof.
MAT200 will be a required course. The proof course is offered at sophomore
level in most four-year institutions to bridge gap between lower level math
courses such as calculus, procedural/computational base, and upper level
math courses such as real analysis and abstract algebra, logical
reasoning/generalization base.
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 4
SUFFOLK COUNTY COMMUNITY COLLEGE
RESPONSE TO PROPOSAL
FROM COLLEGE ASSOCIATE DEAN FOR CURRICULUM
DEVELOPMENT
College Associate Dean for Curriculum Development uses this form to respond to
the proposal with instructions for further developing proposal (e.g., which forms to
use, the campuses and departments who need to be consulted, items to be
considered when developing the proposal.)
******************************************************************
TO:
Elizabeth Chu, Assistant Academic Chair and Professor of
Mathematics
FROM:
Dr. Philip H. Christensen, Associate Dean for Curriculum
Development
DATE:
October 14, 2013
***********************************************************
Comments:
The MAT200: Language, Logic, and Proof course proposal addresses a
current gap in the preparation of our graduates of the Liberal Arts and
Sciences: Mathematics Emphasis / A.A. Degree who transfer to four-year
mathematics programs. This course proposal has emerged from the LAMA
Program Review, conducted in 2009-2011, which recommended this new
course, as well as several other revisions to the current program. (The full
program revision is addressed in a separate Curriculum Revision Proposal.)
As a next step in the course proposal process, you need to complete the
New Course Proposal Form, as found on the College Curriculum Committee
website. Please note: the New Course Proposal Form must include the
votes of the affected department. (Since this course is limited to an
Ammerman Campus program, the faculty affected is the Ammerman
Campus Mathematics / Computer Science Department).
You must also complete the Executive Dean's Acknowledgement of Support
Form and email this form, along with the completed proposal, to the
Ammerman Campus Executive Dean, George Tvelia, as well as a copy to
me, as Associate Dean for Curriculum Development.
The Executive Dean completes this form and returns it to Professor Chu,
with a copy to me. The Executive Dean’s Acknowledgement of Support
should address campus ability and commitment to support this proposal in
terms of the following:
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 5




Academic Merit
Availability Of Personnel
Adequacy Of Facilities
Budgetary Needs For Supplies And Equipment
Please note: the Letter of Intent does not identify MAT200 as a 3-credit
course. This information must appear in the New Course Proposal.
cc:
George Tvelia, Executive Dean, Ammerman Campus
Tina Good, College Curriculum Committee Chair
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 6
SUFFOLK COUNTY COMMUNITY COLLEGE
NEW-COURSE PROPOSAL FORM
ORIGINATING CAMPUS: ( X) Ammerman ( ) Eastern
( ) Grant
Date Submitted to Curriculum Committee: _____10/13_____
To meet the ideals of Suffolk County Community College, new courses should, if appropriate, consider
issues arising from elements of cultural diversity in areas of textbook choice, selection of library and
audio-visual materials, and teaching methodology.
PROPOSER E-MAILS ENTIRE COURSE PROPOSAL PACKET TO THE
APPROPRIATE CURRICULUM COMMITTEE CHAIR AS A WORD DOCUMENT.
Proposal Checklist
Proposer records appropriate departmental votes here and checks to be sure all the documents are
contained within the packet.
(X)
Electronic Letter-of-Intent
(X)
Electronic Letter-of-Support from Executive Dean(s)
(X)
Vote(s) of Department:
Name of Department: Mathematics and Computer Science
For: __26___ Against: _0____
Abstentions: _____
Date of Vote: 10/15/2013 and 10/16/2013 Proposer's Initials: _EC___
Select One: Approved__X___ Not approved_____
Name of Department: _(Name of Department/Campus)_
For: _____
Against: _____
Abstentions: _____
Date of Vote: __________ Proposer's Initials: _____
Select One: Approved_____ Not approved_____
Name of Department: _(Name of Department/Campus)_
For: _____
Against: _____
Abstentions: _____
Date of Vote: __________ Proposer's Initials: _____
Select One: Approved_____ Not approved_____
(X)
Campus Dean Final-Approval Form(s)
(Proposer completes form to this line before sending entire proposal packet to the
appropriate Curriculum Committee Chair)
-------------------------------------------------------------------------------------cc:
Dr. Candice Foley, College Associate Dean for Curriculum Development
Dr. Tina Good, Chair of College Curriculum Committee
Academic Chairs of affected departments
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 7
Curriculum Committee Chair completes form below this line and, upon
approval, the Curriculum Committee Chair e-mails the entire proposal
packet to the College Associate Dean for Curriculum Development, with
electronic copies to the appropriate Executive Deans and the College
Curriculum Committee Chair. (If the proposal is not approved, the Curriculum
Committee Chair e-mails proposer and explains why proposal was not approved and
sends an electronic copy of explanation to the College Curriculum Chair and the
College Associate Dean for Curriculum Development.)
******************************************************************
( )
Vote of Curriculum Committee
Name of Committee:_______________________________
For: _____ Against: _____
Abstentions: _____
Date of Vote: __________
Select One: Approved_____ Not approved_____
( )
Vote of Ammerman Faculty Senate (if appropriate)
For: _____ Against: _____
Abstentions: _____
Date of Vote: __________
Select One: Approved_____ Not approved_____
Abstention_____
( )
Vote of East Congress (if appropriate)
For: _____ Against: _____
Abstentions: _____
Date of Vote: __________
Select One: Approved_____ Not approved_____
Abstention_____
( )
Vote of Grant Assembly (if appropriate)
For: _____ Against: _____
Abstentions: _____
Date of Vote: __________
Select One: Approved_____ Not approved_____
Abstention_____
******************************************************************
Proposal is _____Approved
_____Not Approved
Date________________________________________
Comments:
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Revised 10/2008
New-Course Proposal Form, Pg. 8
NAME OF PROPOSAL: __MAT200 – Language, Logic, and Proof__________
DEPARTMENT/DISCIPLINE:___Mathematics and Computer Science_________
I.
CATALOG DESCRIPTION:
A basic course in the logic of mathematics, the construction of proofs
and writing proofs. The mathematical content is primarily set theory,
logic, number theory, introduction to some basic concepts related to
functions and relations, and some Euclidean Geometry. There is
considerable focus on writing proofs. This course is designed to better
prepare students to take higher level mathematics courses.
II.
STATEMENT OF LEARNING OUTCOMES
(Course outcomes should be stated in the form of what students will be expected to learn in
the course precise, e.g., “Upon successful completion of this course, students will be able to
demonstrate . . . . ”)
Upon successful completion of this course, the student will able to:
A. use logical language, operations, and rules to create and
interpret mathematical proofs.
B. use the definition of sets and maps between them to create and
interpret proofs about sets.
C. use concepts from number theory and elementary Euclidean
geometry to create and interpret proofs from those topics.
D. prove elementary facts about functions and relations.
E. read and critique proofs, and recognize basic errors in reasoning.
F. construct and write mathematical proofs by using methods such
as mathematical induction, proof by contradiction, direct proof,
and proof by contraposition.
III.
RELATIONSHIP TO STUDENTS
A.
Credits and Contact Hours
(Provide a rationale for proposed credits and contact hours. See the formula for credit
hours and contact hours on the Curriculum Website.)
B.
Credit Hours___3___
Contact Hours__3___
Lecture__X___
Studio_____
Lab_____
Internship_____
Course Fees
(Will the student be charged additional fees for this course?)
Lab Fees___N/A_______ Course Fees___N/A_______
Please explain as necessary:____N/A_____________________
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Revised 10/2008
New-Course Proposal Form, Pg. 9
C.
Required/Elective/Restricted Elective
(Will this be a required course? If so, for which curricula? Provide a rationale as to
why this course should be required. If this is proposed as an elective or restricted
elective course, state what elective category it will fulfill and why it is appropriate for
that elective category.)
MAT200 will be a required course in the Liberal Arts and
Sciences, Mathematics Emphasis. The proof course is offered at
the sophomore level in most four-year institutions to bridge the
gap between freshman level math courses, such as calculus,
which are procedural computational based, and upper level math
courses such as real analysis and abstract algebra, which are
based on logical reasoning and generalization.
D.
Prerequisites/Co-requisites
(What prerequisites or co-requisites will be required for this course? Provide a
rationale for these requirements.)
C or better in MAT142 (Calculus II)
Rationale: The proofs course in most colleges is offered in the
third semester of the math major sequence. The prerequisite of
most of the programs at peer institutions as well as the four year
colleges is Calculus II (MAT142).
E.
Transferability
(Would this course transfer to any other institutions? If so, give examples of transfer
institutions/departments who would accept this course. Give the name(s) of the
courses it would transfer as. Demonstrate how transferability was determined.)
This course was modeled after Stony Brook University’s proofs
course. In an e-mail to Dr. Scott Sutherland of the Mathematics
Department at Stony Brook University, he indicated, after
reviewing our proposed syllabus, that our proofs course is
comparable to MAT200, Language, Logic, and Proof – the proofs
course at Stony Brook University.
A copy of the e-mail
correspondence with Dr. Sutherland is attached. (Attachment I)
A similar exchange of correspondence via e-mail took place with
Dr. Barbara Bohannon, Provost of Articulation at Hofstra
University. Dr. Bohannon is also a mathematics professor at
Hofstra University. She forwarded our curriculum revisions to
the Mathematics Chair at Hofstra University, Dr. Gillian Elston,
who reviewed our proposed curriculum revisions and indicated
that MAT200 is similar to their proofs course Math114
Introduction to Higher Mathematics, and hence will transfer. A
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 10
copy of the e-mail correspondence with Dr. Bohannon is
attached. (Attachment II)
ATTACHMENT I
E-mail from Dr. Scott Sutherland, Professor of Mathematics and former Undergraduate
Director at Stony Brook University
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 11
ATTACHMENT II
Email correspondence with Dr. Barbara Bohannon, Associate Provost for Accreditation
and Assessment and Dr. Gillian Elston, Mathematics Chair at Hofstra University
regarding transferability of the proposed Proofs course as well as the proposed curriculum
revisions
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Revised 10/2008
New-Course Proposal Form, Pg. 12
F.
Master Schedule
(How would this course fit into the Master Schedule? How often would it be offered?
Would it be offered in the Fall? Spring? Summer? Winter?)
The initial plan would be to offer the course every fall semester
or every other fall semester, depending on demand.
G.
Estimate of student enrollment
(How many students are anticipated to initially enroll in this course per
semester? Per year? How were these enrollment figures determined?)
20
H.
Class Size
(What is the maximum number of students that should be allowed to enroll in one
section of this course? Provide a rationale for this class size. Should the class size be
forcible?)
The maximum number of students that should be allowed to
enroll in one section of this course is 28.
Rationale: This course is similar in depth and scope to our
Discrete Mathematics course (MAT205) which has a seat limit of
28 students.
IV.
RELATIONSHIP TO FACULTY
A.
Number of current faculty available to teach proposed course and
number of additional faculty required.
The department has 23 mathematics faculty members, almost all
would be available to teach the course. No additional faculty
would be required.
B.
Number of other staff positions required.
None required.
C.
Discipline(s) required and/or minimum preparation in order to teach
the course.
MA or MS or PhD in Mathematics or Applied Mathematics
V.
RELATIONSHIP TO SUNY GENERAL EDUCATION REQUIREMENTS*
Is this course being proposed as a SUNY General Education Course?
YES
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 13
A.
Identify which of the ten SUNY knowledge and skills areas the course
would fulfill.
*The ten SUNY knowledge and skill areas are Mathematics, Natural Sciences,
Social Sciences, American History, Western Civilization, Other World
Civilizations, Humanities, The Arts, Foreign Language, Basic Communication.
Mathematics
B. Demonstrate how the course outcomes map to the SUNY Learning
Outcomes for the knowledge and skills areas you have identified. (See
the Curriculum Website for further details about the required
outcomes.)
SUNY Learning Outcomes- Mathematics
Students will demonstrate the ability to:





interpret and draw inferences from mathematical models such as
formulas, graphs, tables and schematics; (SLO A and B)
represent mathematical information symbolically, visually, numerically
and verbally; (SLO F)
employ quantitative methods such as, arithmetic, algebra, geometry,
or statistics to solve problems; (SLO C and D)
estimate and check mathematical results for reasonableness; (SLO E)
and
recognize the limits of mathematical and statistical methods. (SLO F)
MAT200 – Students Learning Outcomes (SLO)
Upon successful completion of this course, the student will able to:
A. use logical language, operations, and rules to create and
interpret mathematical proofs.
B. use the definition of sets and maps between them to create and
interpret proofs about sets.
C. use concepts from number theory and elementary Euclidean
geometry to create and interpret proofs from those topics.
D. prove elementary facts about functions and relations.
E. read and critique proofs, and recognize basic errors in reasoning.
F. construct and write mathematical proofs by using methods such
as mathematical induction, proof by contradiction, direct proof,
and proof by contraposition.
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 14
C.
How does this course incorporate the SUNY infused competencies of
Critical Thinking and Information Management? (See the Curriculum
Website for further details about the required outcomes for
Information Management and Critical Thinking.)
This course incorporates the SUNY infused competencies of
Critical Thinking by requiring the students to:


identify, analyze, and evaluate arguments as they occur in their own
or others' work; and
develop well-reasoned arguments.
The nature of the course is such that it requires the students to read
and critique proofs, and recognize basic errors in reasoning. This is
just one of the student learning outcomes of this course.
D.
Do the faculty within the department/discipline agree to assess this
course according to the approved *SUNY General Education
Assessment Plan, using assessment measures, i.e., instruments that
measure the attainment of student learning outcomes as described in
the plan?
*Be sure to see if the original assessment plan has been updated either through the
strengthened campus-based assessment plan or through a closing-the-loop process.
Contact Dr. Allen Jacobs, College Associate Dean for Assessment of Academic and
Student Affairs for further information.
Yes
VI.
COSTS
List costs and space requirements.
The cost of staffing this course is approximately $3,600- the
equivalent of adjunct pay for teaching a 3-credit course.
VII.
COURSE SYLLABUS
(See Appendix Below.)
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 15
SUFFOLK COUNTY COMMUNITY COLLEGE
COLLEGE COURSE SYLLABUS FORM
To meet the ideals of Suffolk County Community College, new courses should, if appropriate, consider
issues arising from elements of cultural diversity in areas of textbook choice, selection of library and
audio-visual materials, and teaching methodology. (Please note that a course syllabus is not the same
as a course outline. A course syllabus outlines the general requirements for a course. A course
outline is the specific document created by the individual faculty member to distribute to a specific
course section. Please see the Faculty Handbook for further details as to what to include in a course
outline. A SAMPLE course outline should be attached below.)
I.
Course Number and Title:
(Be sure to consider whether this course is a 100- or 200-level course and give a
rationale for the decision.)
MAT 200 Language, Logic and Proof
Rationale: This course is usually taken in the third semester in many
mathematics curricula. The committee modeled this proofs course
after the one offered at Stony Brook University, and their course is a
sophomore level course, numbered MAT200.
II.
Catalog Description:
A basic course in the logic of mathematics, the construction of proofs
and writing proofs. The mathematical content is primarily set theory,
logic, number theory, introduction to basic analysis, and Euclidean
Geometry. There is considerable focus on writing proofs.
A/ 3 cr. hrs.
III.
*Learning Outcomes: (Main concepts, principles, and skills
you want students to learn from this course)
Upon completion of this course, students will be able to:
A. use logical language, operations, and rules to create and interpret
mathematical proofs.
B. use the definition of sets and maps between them to create and
interpret proofs about sets.
C. use concepts from number theory and elementary Euclidean
geometry to create and interpret proofs from those topics.
D. prove elementary facts about functions and relations.
E. read and critique proofs, and recognize basic errors in reasoning.
F. construct and write mathematical proofs by using methods, such as
mathematical induction, proof by contradiction, direct proof, and
proof by contraposition.
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 16
IV.
Programs that Require this Course: (List or indicate none.)
Liberal Arts and Sciences: Mathematics Emphasis (LAMA-AA)
V.
Major Topics Required:
Approximate
Time
(Including
Examinations)
Required Topics
A. Introduction: A more rigorous approach to the familiar
(revisit topics from algebra, real numbers, and calculus with an
emphasis on understanding “why?” rather than “how”)
Selections can be chosen from the list below or from other proofs
found in earlier mathematics courses:
1. Proving the quadratic formula both algebraically and
geometrically.
2. Deriving a formula for solving a system of 2 simultaneous linear
equations in 2 unknowns.
3. Proving
1
1
weeks
2
3
1
weeks
2
3
1
weeks
2
2 is irrational.
4. Precise definition of limit and proving lim f ( x)  L
x a
for linear functions.
5. The Binomial Theorem and proofs of the power, product and
quotient rules for differentiation.
6. Showing that differentiable at a point implies continuous at a
point.
7. Finding counterexamples.
B. Logic
1. Statement, compound statements and truth values
2. Truth tables, logical equivalence, tautologies and contradictions
3. Conditional statements and their negation
4. Converse, inverse and contrapositive of conditional statements
5. Valid argument forms (rules of inference)
6. Proving arguments valid using truth tables
7. Proving arguments valid using the rules of inference
8. Brief introduction to universal and existential quantifiers and
learning how to negate these quantifiers
C. Elementary Number Theory
1. Natural numbers, integers, rational numbers, irrational numbers
and real numbers
2. Formal definition of even, odd, prime, composite, and “a divides
b”
3. Quotient-Remainder Theorem
4. Euclidean Algorithm
5. Methods of proof illustrated by intuitive number theory results
(direct proofs, proof by contradiction, proof by contraposition,
proof by division into cases, uniqueness and existence proofs)
6. Mathematical induction
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 17
D. Set Theory
1. Basic definitions (set, set equality, operation on sets, empty set,
partitions of sets, power sets, Cartesian product)
2. Basic set identities and their proofs
3. Disproving set properties
4. Proving that a set is an empty set
E. Functions (Provide an understanding of what a function is and prove
basic results)
1. Definition of a function and connections with set theory
2. Notion of well-defined
3. One-to-one, onto and inverse functions
4. Composition of functions
F. Relations
1. Relations on sets
2. Reflexivity, symmetry and transitivity
3. Equivalence relations
4. Relation induced by a partition
5. Equivalence classes
6. Showing every equivalence relation induces a Partition
7. Connection between functions and relations
G. Optional Topic
1. Introduction to Euclidean Geometry
a. Introduction to axiomatic systems
b. Proofs by construction involving circles, lines and triangles
2. Properties of continuous function
VI.
2 weeks
2 weeks
2
1
weeks
2
Special Instructions:
A. Prerequisite(s) to this Course: (List or indicate none)
C or better in MAT142 (Calculus II)
B. Course(s) that Require this Course as a Prerequisite:
(List courses or indicate none)
None
C. External Jurisdiction: (List credentialing organization/association if
appropriate or indicate none.)
None
VII.
Supporting Information: (Examples – newspapers, journals,
Internet resources, CD-ROMS, Videos, other teaching materials, textbooks, etc.)
Textbook to be determined by the instructor teaching the course.
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Revised 10/2008
New-Course Proposal Form, Pg. 18
VIII.
Optional Topics: (List or indicate none)
1.
2.
IX.
Introduction to Euclidean Geometry
a.
Introduction to axiomatic systems
b.
Proofs by construction involving circles, lines and
triangles
Properties of continuous function
Evaluation of Student Performance:
List possible methods to be used for evaluating students’ achievement of the
course’s learning outcomes.
midterms
Oral presentation
80%
20%
100%
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 19
X.
Sample Course Outline
(See Faculty Handbook online at http://depthome.sunysuffolk.edu/FacultyHandbook/
for guidelines.)
SUFFOLK COUNTY COMMUNITY COLLEGE
DEPARTMENT OF MATHEMATICS and COMPUTER SCIENCE
MAT200
Course Outline
Fall 2014
Instructor:
Section:
Course: Language, Logic and Proof
CRN:
Time and Location:
Prerequisites: C or better in MAT142 Calculus II
Telephone:
E-mail:
If an e-mail is sent, be sure to send out from your college account and
identify yourself in the “subject” line. Unidentified e-mail is assumed to
be a virus, and is deleted without being opened.
Office hours:
COURSE OBJECTIVES:
Upon successful completion of this course, the student will able to:
A. use logical language, operations, and rules to create and interpret
mathematical proofs.
B. use the definition of sets and maps between them to create and interpret
proofs about sets.
C. use concepts from number theory and elementary Euclidean geometry to
create and interpret proofs from those topics.
D. prove elementary facts about functions and relations.
E. read and critique proofs, and recognize basic errors in reasoning.
F. construct and write mathematical proofs by using methods, such as;
mathematical induction, proof by contradiction, direct proof, and proof by
contraposition.
GRADING PRACTICE
Students are expected to take all examinations. No make up tests will be given.
Missing exams receive a grade of zero.
Every student must take the oral
examination in order to receive a passing grade for this course. If a student misses
more than one exam, he/she will be withdrawn from the class.
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 20
COURSE GRADE:
There will be two midterms (80%) and one oral presentation (20%).
Letter grades will be assigned based on the course average as follows:
A: 90% and above
C: 70%-74%
B+: 85% - 89%
D+: 65% - 69%
B: 80% - 84%
D: 60% - 64%
C+: 75% - 79%
F: below 60%
College-Wide Attendance Policy:
All students are expected to attend every session of each course for which they are
registered. Students are responsible for all that transpires in class whether or not
they are in attendance. The College defines excessive absence or lateness as more
than the equivalent of one week of class meetings during the semester. Excessive
absence or lateness may lead to failure in a course or removal from the class
roster.
INSTRUCTOR’S ATTENDANCE POLICY:
Attendance at all classes is highly recommended. If more than three absences
occur, the students may be withdrawn from the course. Absence from class on the
day of an exam will be deemed the equivalent of having taken the test and
receiving a “zero” on it.
TEXTBOOK:
TITLE:
AUTHOR:
PUBLISHER:
ISBN:
OUTLINE OF TOPICS
Week 1
Introduction - part I
Week 2
Introduction – Part II. Compound statements and truth values.
Week 3
Truth table and conditional statements and their negation.
Week 4
Converse, inverse, and contrapositive statements; valid argument form.
Week 5
Week 6
Proving arguments valid using the truth tables and rules of inference.
Number system and formal definition of even, odd, prime and composite
numbers; Quotient and remainder theorem.
Week 7
Week 8
Euclidean Algorithm and method of proof in number theory – direct proof,
proof by contradiction and proof by contraposition.
Uniqueness and existence proof and mathematical induction.
Midterm 1
Week 9
Mathematical induction and basic definitions in set theory.
Week 10
Basic set identities and their proof. Disproving set properties.
Week 11
Proving that a set is an empty set. Definition of function and connection with
set theory.
Week 12
Notion of well defined function and one-to-one, onto and inverse functions
Week 13
Composition of function and relations on sets. reflexivity, symmetry and
transivity.
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 21
Week 14
Week 15
Optional
1.
2.
Equivalence relations, relation induced by a partition, equivalence classes.
Connection between functions and relations.
Midterm 2
Student oral presentations.
Topics: (If time permits)
Introduction to Euclidean Geometry
c. Introduction to axiomatic systems
d. Proofs by construction involving circles, lines and triangles
Properties of continuous function
MISCELLANEOUS:
1. No text-messaging!!!
2. Students should seek help when needed by visiting their instructor or the
Math Learning Center [MLC, (631)451-4002] in R-235. The MLC hours are
Mon. through Thurs.: 9 am ~ 6 pm; Fri.: 9 am ~ 2 pm; Sat.: 9 am ~ 1 pm.
3. Disruptions such as talking, eating, leaving and re-entering the room
regularly and electronic devices frequently going off will not be tolerated.
The instructor reserves the right (by college policy) to ask a disruptive
student to leave the classroom for the day.
4. If you are a student who has a disability and is entitled to reasonable
accommodations, please speak to me privately outside of class as soon as
possible so that the accommodations can be in place in a timely fashion. If
you have specific questions about obtaining these services, you can contact a
special-needs counselor.
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008
New-Course Proposal Form, Pg. 22
SUFFOLK COUNTY COMMUNITY COLLEGE
EXECUTIVE DEAN’S ACKNOWLEDGMENT-OF-SUPPORT
The Proposer should email completed proposal packet along with the Executive Dean’s
Acknowledgment-of-Support Form. The Proposer should complete the top half of the form and the
Executive Dean should check the “Support” or “Do Not Support” line based on the Campus’ ability to
commit to implementing the proposal if it is approved through the Governance process.
Criteria to consider for supporting this proposal are listed below. If the Executive Dean is in general
support of the proposal but has specific concerns related to the proposal, these concerns should be
stated in the comment section. If the Executive Dean does not support the proposal, specific reasons
should be listed in the comment section.
The Executive Dean should email completed form to Proposer so that it can be included in the
proposal packet to be submitted to the College Curriculum Committee Chair.
******************************************************************
The Executive Dean’s Acknowledgement-of Support is a commitment to
support the implementation of the course adoption in terms of:
 Academic Merit
 Availability of Personnel
 Adequacy of Facilities
 Budgetary Needs for Supplies and Equipment
******************************************************************
This section to be filled out by Proposer:
Name of Proposal: _ MAT200 – Language, Logic, and Proof
Adopting Campus:
A_X___
E____
G_____
************************************************************************
This section to be filled out by Executive Dean:
____ X_____Support
__________Do Not Support
Name of Executive Dean:__George P. Tvelia______________________________
Date__10/18/13__________________________
Comments:
This proposed course will better prepare our math majors for the upper level math
courses they will be taking in their junior and senior years.
ALL FORMS MUST BE SUBMITTED ELECTRONICALLY
Revised 10/2008