INTRODUCTION TO MATHEMATICAL REASONING: PREPARATION FOR ENTRY INTO HIGHER EDUCATION

PRESENTATION:
The methods and tools employed in mathematical reasoning are a crucial part of a student’s toolbox. Much more than just arithmetical ability, the quality and rigor involved in reasoning are the cornerstone for solving any exercise, problem or demonstration. Learning the right methods and practices in reasoning early on allows for easier integration into higher education and provides a solid base for following your curriculum.

This Mathematics MOOC meets the dual goal of supporting you in the transition from high school to further education, and allowing you to revise and consolidate the knowledge you gained from the first year of your Grande École preparatory class or university study.

Its approach is to give you a gradual introduction to mathematical reasoning, from the most basic notions right through to more complex concepts.

This four-week course is divided into theory sessions, which use explanatory videos and hands-on exercises in order to progress step by step.

The assessments proposed at the end of the module ensure that students have mastered the concepts observed and practiced in class. The discussion forum is a great space for collective learning.

BY THE END OF THE MOOC, YOU WILL BE ABLE TO:

understand the mechanisms involved in mathematical reasoning
practice mathematical reasoning automatically
identify the appropriate method(s) of solving any problem or situation
apply reasoning methods intelligently
gain autonomy in mathematical reasoning and demonstrations
CERTIFICATION

A certificate of successful completion is awarded by FUN to students who pass the assessments.


COURSE SYLLABUS

WEEK 1: Naïve set theory
1.1 Sets and subsets
1.2 Operations on sets
1.3 Properties: distributivity and De Morgan’s laws
1.4 Power sets, cardinality
WEEK 2: Connectives and quantifiers
2.1 Predicates, formulas and properties
2.2 Logical connectives: negation, conjunction and disjunction
2.3 Implication
2.4 Equivalence
2.5 Quantifiers
2.6 Connectives and quantifiers
WEEK 3: Mathematical reasoning and demonstration methods
3.1 Axioms, definition, theorem
3.2 Direct methods
3.3 Indirect methods
3.4 Recurrence and its variants
3.5 Equivalence reasoning and analysis-synthesis method
WEEK 4: Applications of sets
4.1 Applications
4.2 Injections and surjections
4.3 Bijections
4.4 Direct images and inverse images
4.5 Corrected problem