Campus Location:
Effective Date: 2014-51
Course Number and Title:
MAT 285 Introduction to Proof
Pre-requisites:
MAT 263 and MAT 281
Course Hours and Credits:
4
4
1
Course Description:
Required Text(s):
Credits
Lecture Hours/week
Lab Hours/week
This course provides a transition from computational mathematics to abstract,
proof based mathematics. The primary focus of the course will be the
development of skills to read, understand, and produce proofs of mathematics
statements. Topics include set theory, functions, relations, cardinality, the order
properties of real numbers, least upper bound, greatest lower bound, the
completeness axiom, and limits.
Obtain current textbook information at https://www.dtcc.edu/studentresources/bookstores or www.dtcc.edu/allschedules or by visiting the bookstore.
You will need to know the course number and section.
Additional Materials:
Method of Instruction:
Face-to-Face
Disclaimer:
Core Course Performance Objectives:
1. Translate formal mathematical statements that are written in the standard language and symbolism used by
mathematicians. (CCC 1, 2, 4, 7; PGC 2)
2. Evaluate the validity of a proposed formal mathematical proof. (CCC 1, 2, 4, 7; PGC 2)
3. Categorize, identify, and examine common techniques used in constructing mathematical proofs.
(CCC 1, 2, 4, 7; PGC 2)
4. Communicate a formal mathematical proof. (CCC 1, 2, 4, 6, 7; PGC 2, 4)
See Core Curriculum Competencies (CCC) and Program Graduate Competencies (PGC) at the end of the syllabus.
Course objectives are coded to the competency(cies) they develop.
Measurable Performance Objectives:
Upon completion of the course, the student will:
1. Translate formal mathematical statements that are written in the standard language and symbolism
used by mathematicians.
1.1 Analyze the essential components of a mathematical statement.
1.2 Utilize formal mathematics definitions, quantifiers, and terminologies to deduce content of
mathematical statements.
1.3 Apply logic to a mathematical statement to determine its truth value.
2.
Evaluate the validity of a proposed formal mathematical proof.
2.1 Read and synthesize a formal proof into language that is easily understood.
2.2 Scrutinize a mathematical proof in order to verify its validity.
2.3 Expand the deductive argument in a formal proof to better communicate the line of reasoning.
3. Categorize, identify, and examine common techniques used in constructing mathematical proofs.
3.1 Analyze mathematical statements and choose the most effective strategy to support its validity.
3.2 Utilize the contrapositive and contradiction to support the validity of a mathematical argument.
3.3 Apply the principles of induction to logical argument.
3.4 Analyze a logical argument using cases.
3.5 Apply logical methods to proofs involving least upper bound and greatest lower bound.
3.6 Develop strategies to prove existence or uniqueness.
4.
Communicate a formal mathematical proof.
4.1 Integrate accepted mathematical techniques to construct a formal mathematical proof.
4.2 Write a mathematical proof with sufficient explanation and logic.
4.3 Produce a written proof using acceptable word processing software that captures correct
mathematical symbolism.
Evaluation Criteria/Policies:
Students will demonstrate proficiency on all measurable performance objectives at least to the 75% level.
College Grading System
92-100
=
A
83-91
=
B
75-82
=
C
0-74
=
F
Students should refer to the Student Handbook for information on Academic Standing Policy, Academic Honesty
Policy, Student Rights and Responsibilities, and other policies relevant to their academic progress.
Core Curriculum Competencies: (The competencies every graduate will develop)
1. Communicate clearly and effectively both orally and in writing.
2. Demonstrate effective problem solving and reasoning skills.
3. Work effectively in groups of people from diverse backgrounds.
4. Demonstrate ethical and professional understanding and conduct.
5. Apply appropriate information literacy skills to locate, evaluate and use information effectively.
6. Use computer technology appropriate to the field.
7. Use scientific and mathematical reasoning appropriate to the technology.
Program Graduate Competencies: (The competencies every graduate will develop specific to his/her major.)
1.
2.
3.
4.
Employ mathematical strategies to solve algebraic, geometric, trigonometric and calculus problems.
Prove or disprove mathematical statements using formal arguments.
Apply knowledge of the physical, social, emotional and cognitive development of adolescents.
Access and implement educational technology.