Objectives of Programme's Learning Outcomes

• Understand "elementary" mathematics profoundly
• Use vector spaces, linear applications and the techniques associated with them
• Understand and use the naive set theory
• Understand basic algebraic structures
• Manipulate previously acquired knowledge that appears in a question
• Give examples and counterexamples for definitions, properties, theorems, etc.
• Understand and produce strict mathematical reasoning
• Write clearly and concisely
• Use mathematical vocabulary and formalism appropriately
• Make sense of formal expressions
• Rely on a picture to illustrate a concept, rationale, etc.
• Solve new problems
• Abstract and manipulate theories and use these to solve problems
• Adapt an argument to a similar situation
• Use knowledge from different fields to address issues

Learning Outcomes of UE

Basic algebra: groups, commutative rings, fields. 
This course aims to present the essential material in undergraduate basic algebra. 

Content of UE

Groups: generated subgroups, factorisation of morphisms, canonical isomorphisms, centralisers, normalisers, dihedral groups, quaternion group, linear groups over finite fields. 
Commutative rings: prime ideals, maximal ideals, operations on ideals, Chinese remainder theorem, euclidean rings, PID's, UFD's. 
Fields: field extensions, multiplicativity of degrees, algebraic and transcendental elements, roots of unity, minimal polynomials, extension degree computations. 

Prior Experience

"Algèbre I" course.

Type of Assessment for UE in Q2

• Written examination

Q2 UE Assessment Comments

Not applicable

Type of Assessment for UE in Q3

• Written examination

Q3 UE Assessment Comments

Not applicable