Mathematical Reasoning – Foundations Course for Math Majors
A course in Mathematical Reasoning and Proofs must be taken by every mathematics major in every University in United States. This course is usually taken in the first semester of a junior year. It introduces topics in upper-level mathematics such as logic, set theory, mathematical reasoning and proofs, relations and functions, elements of number theory, Induction and Recursion, Graphs and Trees, and Boolean Algebra. This course prepares mathematics students for successful transition to upper-level University courses in Mathematics, Science, and Engineering, or any field where you need to use logic, clear thinking, and higher-level cognitive skills.
The following are Virginia Universities that attract most of our transferring students. Each of these Universities has an introductory course to Higher Mathematics. Such course is required for all math majors.
Virginia Commonwealth University:
MATH 300 Introduction to Mathematical Reasoning. 3 Hours.
An introduction to basic concepts of mathematical reasoning and the writing of proofs in an elementary setting. Direct, indirect and induction proofs. Illustrations of the concepts include basic proofs from mathematical logic, elementary set theory, elementary number theory, number systems, foundations of calculus, relations, equivalence relations, functions and counting with emphasis on combinatorial proofs.
Virginia Tech:
3034 Introduction to Proofs
Practice in writing mathematical proofs. Exercises from set theory, number theory, and functions. Specific topics include set operations, equivalence relations, mathematical induction, the division algorithm and images and pre-images of sets
University of Virginia:
MATH 3000 – Transition to Higher Mathematics
Covers basic concepts with an emphasis on writing mathematical proofs. Topics include logic, sets, functions and relations, equivalence relations and partitions, induction, and cardinality.
William and Mary:
MATH 214 – Foundations of Mathematics
Fundamentals of advanced mathematics: Propositional logic, quantifiers and methods of proof; naive set theory including mathematical induction, relations, orders, functions, and countability.
Old Dominion University:
MATH 300. Number Systems.
Sets and systems of numbers, prime, integer, rational, irrational, real, complex and their properties. Representation of numbers. Divisibility, congruence, modular arithmetic, elementary number theory and symbolic logic.
Mary Washington University:
MATH 330 – Foundations of Advanced Mathematics
Introduction to mathematical reasoning and rigor. Includes topics such as basic logic, set theory, mathematical induction, relations, functions, sequences, cardinality, elementary number theory, and axiomatic construction of the real numbers. Emphasis placed on reading mathematics, understanding mathematical concepts, and writing proofs.
Christopher Newport University:
MATH 245. Proofs and Discrete Mathematics
Topics are presented so as to develop facility with methods of proof and mathematical argument. Topics will include logic, sets, binary relations, functions, binary operations, elementary number theory, number bases, mathematical induction, recursive definitions and algorithms.