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DESCRIPTION: MAT 2571 prepares students for an advanced mathematics curriculum by providing a foundation to proofs in abstract mathematics. Topics include propositional and first order logic, axiomatic approach to number theory, set theory, and abstract properties of relations, with a particular emphasis on number theory. The course focuses on the processes of mathematical argumentation and reasoning, deduction, and discovery.
TEXT: Book of Proof. (Edition 2, Creative attribution -No Derivative Works 3.0) by R. Hammack.
PRE/COREQUISITES: MAT 1575
Revised by Professors A. Masuda, J. Reitz and S. Singh (2018)
NEW YORK CITY COLLEGE OF TECHNOLOGY
The City University of New York
DEPARTMENT: Mathematics
COURSE: MAT 2571
TITLE: Introduction to Proofs
CREDITS: 4 (4 class hours)
GRADING PROCEDURE: Homework assignments; exams; group and individual projects; presentations.
GRADING POLICY: Projects, presentations, group work and individual writing assignments 25% Homework 20% In-class exams 30% Final exam 25%
Course Intended Learning Outcomes/Assessment Methods
Learning Outcomes Assessment Methods
1. Evaluate truth of statements in propositional and first-order logic.
Tests, group work, written assignments, projects, presentations.
2. Reason in accordance with laws of propositional and first-order logic.
Tests, group work, written assignments, projects, presentations.
3. Use the axiomatic method in establishing the truth of mathematical statements.
Tests, group work, written assignments, projects, presentations.
4. Analyze and prove elementary statements with an emphasis on group theory, number theory and set theory.
Tests, group work, written assignments, projects, presentations.
General Education Learning Outcomes/Assessment Methods
Learning Outcomes Assessment Methods
1. Understand and employ both quantitative and qualitative analysis to solve problems.
Tests, group work, written assignments, projects, presentations.
2. Employ scientific reasoning and logical thinking. Tests, group work, written assignments, projects, presentations. 3. Communicate effectively using written and oral means.
Tests, group work, written assignments, projects, presentations.
4. Use creativity to solve problems. Tests, group work, written assignments, projects, presentations.
New York City College of Technology Policy on Academic Integrity
Students and all others who work with information, ideas, texts, images, music, inventions, and other intellectual property owe their audience and sources accuracy and honesty in using, crediting, and citing sources. As a community of intellectual and professional workers, the College recognizes its responsibility for providing instruction in information literacy and academic integrity, offering models of good practice, and responding vigilantly and appropriately to infractions of academic integrity. Accordingly, academic dishonesty is prohibited in The City University of New York and at New York City College of Technology and is punishable by penalties, including failing grades, suspension, and expulsion. The complete text of the College policy on Academic Integrity may be found in the catalog.
