Course Number and Title: MAT 285 Introduction to Proof
This course provides a transition from computational mathematics to abstract, proof-based mathematics. The primary focus of the course is the development of skills to read, understand, and produce proofs of mathematical statements that explore key concepts from number theory, algebra, and analysis. Topics include set theory, functions, relations, order properties of real numbers, least upper bound, greatest lower bound, the completeness axiom, and limits.
- Translate formal mathematical statements that are written in the standard language and symbolism used by mathematicians. (CCC 1, 2, 4, 6; PGC 2)
- Categorize, identify, and examine common techniques used in constructing mathematical proofs. (CCC 1, 2, 4, 6; PGC 2)
- Communicate a formal mathematical proof. (CCC 1, 2, 4, 6; PGC 2, 4)
- Evaluate the validity of a proposed formal mathematical proof. (CCC 1, 2, 4, 6; PGC 2)
See Core Curriculum Competencies and Program Graduate Competencies at the end of the syllabus. CCPOs are linked to every competency they develop.
Upon completion of this course, the student will:
- Translate formal mathematical statements that are written in the standard language and symbolism used by mathematicians.
- Analyze the essential components of a mathematical statement.
- Use formal mathematical definitions to deconstruct mathematical statements.
- Apply logical connectives and quantifiers to evaluate mathematical statements.
- Categorize, identify, and examine common techniques used in constructing mathematical proofs.
- Analyze mathematical statements to construct a logical structure for a proof.
- Apply direct proof methods to show the validity of mathematical arguments.
- Use indirect proof methods, including contraposition and contrapositive, to show the validity of mathematical arguments.
- Apply the principles of induction to logical argument.
- Analyze a logical argument using cases.
- Communicate a formal mathematical proof.
- Integrate accepted mathematical techniques to construct a formal mathematical proof.
- Write a mathematical proof with sufficient explanation and logic.
- Produce a written proof using acceptable word processing software that captures correct mathematical symbolism.
- Evaluate the validity of a proposed formal mathematical proof.
- Read and synthesize a formal proof into language that is easily understood.
- Scrutinize a mathematical proof in order to verify its validity.
- Expand the deductive argument in a formal proof to better communicate the line of reasoning.
Students must demonstrate proficiency on all CCPOs at a minimal 75 percent level to successfully complete the course. The grade will be determined using the Delaware Tech grading system:
Students should refer to the Student Handbook for information on the Academic Standing Policy, the Academic Integrity Policy, Student Rights and Responsibilities, and other policies relevant to their academic progress.
- Apply clear and effective communication skills.
- Use critical thinking to solve problems.
- Collaborate to achieve a common goal.
- Demonstrate professional and ethical conduct.
- Use information literacy for effective vocational and/or academic research.
- Apply quantitative reasoning and/or scientific inquiry to solve practical problems.
- 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.
The College is committed to providing reasonable accommodations for students with disabilities. Students are encouraged to schedule an appointment with the campus Disabilities Support Counselor to request an accommodation needed due to a disability. A listing of campus Disabilities Support Counselors and contact information can be found at the disabilities services web page or visit the campus Advising Center.