## Study.com | Evaluated Learning Experience

## Math 97: Introduction to Mathematical Reasoning

Varies; self-paced.

June 2012 - December 2022.

Upon successful completion of the course, students will be able to: solve basic logic problems and mathematical proofs, explaining the reasoning behind the solution; identify and compare different types of sets and their representation, including finite, infinite, countable, and uncountable sets; demonstrate techniques for performing operations and solving equations with rational and irrational numbers; differentiate between relations and functions, and determine if a function is an injection, surjection, or bijection; write equations to calculate combinations and permutations and use those equations to solve problems; measure the angles of a triangle and use indirect proofs to prove two lines are parallel; construct a geometric proof to determine the validity of a statement; calculate the area of basic geometric shapes such as triangles, quadrilaterals, polygons, and circles; compare figures to determine if they are symmetrical.

The course is self-paced. Instruction is delivered through online video and text lessons. Students are assessed through quizzes and a proctored final exam. Topics include: introduction to logic in math; mathematic inductions; types of proofs in math; numerical problem solving skills; principles of mathematical sets; groups and sets in algebra; number theory overview; rational and irrational numbers overview; order relations and functions; mathematical combinations; informal geometry and measurement; acute, obtuse and right angles; parallel lines in geometry; geometric postulates and proofs; triangle types and theorems; proportions and similar triangles; types of quadrilaterals; introduction to circles; area of polygons and circles; surfaces and solids; symmetry and transformations.

In the associate/certificate degree category, 4 semester hours in General Math or as a general elective (6/17).