Prerequisite: MATH 132, or equivalent, with grade C- or better

Course Learning Outcomes: By the end of this course, students will be able to:

• Write and interpret mathematical notation and mathematical definitions,
• Formulate and interpret statements presented in Boolean logic,
• Reformulate statements from common language to formal logic,
• Apply truth tables and the rules of propositional and predicate calculus,
• Formulate short proofs using the following methods: direct proof, indirect proof, proof by contradiction, and case analysis,
• Construct direct and indirect proofs and proofs by induction and determine the appropriateness of each type in a particular setting,
• Apply the logical structure of proofs and work symbolically with connectives and quantifiers to produce logically valid, correct and clear arguments,
• Analyze and critique proofs with respect to logic and correctness,
• Unravel abstract definitions, create intuition-forming examples or counterexamples, and prove conjectures,
• Write solutions to problems and proofs of theorems that meet rigorous standards,
• Demonstrate a working knowledge of set notation and elementary set theory, recognize the connection between set operations and logic, prove elementary results involving sets, and explain Russell's paradox,
• Perform set operations on finite and infinite collections of sets and be familiar with properties of set operations,
• Determine equivalence relations on sets and equivalence classes,
• Apply different properties of injections, surjections, bijections, compositions, direct and inverse images and inverse functions,
• Define and interpret the concepts of divisibility, congruence, greatest common divisor, prime, and prime-factorization,
• Produce rigorous arguments (proofs) centered on the material of number theory, most notably in the use of mathematical induction, and the Well Ordering Principle in the proof of theorems.

Program Learning Outcomes and Mission Statement of the Department of Mathematics

Course Requirements

• Textbook (required): R. J. Bond and W. J. Keane, An Introduction to Abstract Mathematics, Brooks/Cole, 1999
• Lecture Notes
• Goals and Objectives of the Course: The purpose of this course is to study the basic concepts of mathematics such as: mathematical proofs, set theory, mathematical induction and recursion, binary relations, functions, definition and development of some common number systems, cardinal numbers, abstract algebra.
• Class Procedures: The majority of each class period will be lecture oriented. You are expected to: attend the lectures and to take your own lecture notes, read the textbook and work out problems from that section covered in class, do the homework problems.
• Attendance Requirements: It is important that you attend every class scheduled for this course. You are responsible for all announcements and material covered in this class as well as material from the textbook which is assigned but not covered in class.
• Computers: Any electronic devices such as laptops, tablets and cell phones cannot be used during the class. Please set your cell phones on vibrate.

Grading

• Homework: There will be weekly homework assignments that will count for 25% of the grade.
• Tests: There will be two midterms tests and a final exam. Each test will count for 25% of the total grade.
• Make-ups: Make-up exams will be given only in cases of extremely properly documented emergencies. Late homework will not be accepted.
• Evaluation: Grades will be determined on a 100 point scale. Those point totals near cutoff will be individually considered for the next higher grade. I do reserve the right to add some extra points depending on the class participation and outstanding exam performance.

Changes: The course plan may be modified during the semester. Such modifications will be announced in advance during class periods. You are responsible for keeping abreast of such changes.

Remarks: It is important to note that this course is cumulative (builds on itself) and it is assumed that all earlier parts covered are liable for any exam. It is strongly advised that you start working on this course from the very beginning. The course moves at a fast place, so it is very hard to catch up if you get behind.

Counseling and Disability Services. Reasonable Accommodations: New Mexico Tech is committed to protecting the rights of individuals with disabilities. Qualified individuals who require reasonable accommodations are invited to make their needs known to the Office of Counseling and Disability Services (OCDS) as soon as possible. In addition, New Mexico Tech offers mental health and substance abuse counseling through the Office of Counseling and Disability Services. The confidential services are provided free of charge by licensed professionals. To schedule an appointment, please call 835-6619.