MAT3013
Foundations of Mathematics (30) 3 Credit Hours
Course Catalog
MAT 3013. Foundations of Mathematics. (30) 3 Credit Hours.
Prerequisite: MAT1214. Development of theoretical tools for rigorous mathematics. Topics may include mathematical logic, propositional and predicate calculus, set theory, functions and relations, cardinal and ordinal numbers, Boolean algebras, and construction of the natural numbers, integers, and rational numbers. Emphasis on theorem proving. (Formerly MAT2243. Credit cannot be earned for MAT3013 and MAT2243.) Generally offered: Fall, Spring, Summer. Differential Tuition: $150.
Description
Foundations of Mathematics is a pivotal course for mathematics majors. It serves as the first major step towards modern mathematics of rigorous proofs and a true prerequisite to real analysis and abstract algebra. Up to this point students are asked to do few proofs (notably geometry and perhaps some epsilondelta in calculus). The course particularly emphasizes settheoretical constructions, such as functions, composition, inversion, forward and inverse images, relations, equivalence relations, partial orders, quotient sets and products and unions of sets, vital to further work in mathematics.
Evaluation
 No makeup exams are offered.
 An absence may be excused if sufficient evidence of extenuating circumstances is provided. In this case, the final exam grade
could be used as the grade for the missed exam.
 Students will have access to several past exams for practice.
Text
 Ethan D. Bloch, Proofs and Fundamentals: A First Course in Abstract Mathematics, 2nd ed, Springer (2011). https://linkspringercom.libweb.lib.utsa.edu/book/10.1007%2F9781441971272
Topics List
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