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Topology
University of Galway - Direct Enroll Program
Galway, Ireland
Dates: 1/7/25 - 5/11/25
Topology
OVERVIEW
CEA CAPA Partner Institution: University of Galway
Location: Galway, Ireland
Primary Subject Area: Mathematics
Instruction in: English
Course Code: MA342
Transcript Source: Partner Institution
Course Details: Level 300
Recommended Semester Credits: 2.5
Contact Hours: 36
DESCRIPTION
An introduction to the theory and application of topology.
Learning Outcomes
1. Understand and use the basic algebra of set theory, including De Morgan's Laws
2. State the definition of a topological space and describe several examples of this concept
3. Explain the relationship between topologies and continuous functions
4. Understand the concept of homeomorphism
5. Construct new topological spaces using the subspace and quotient constructions
6. Understand and explain the concept of compactness, prove some basic theorems relating to this concept
7. Understand and explain the concept of connectedness, prove some basic theorems relating to this concept
8. Apply topological ideas to solve problems in other areas of mathematics or applied mathematics e.g. topological proof of the fundamental theorem of algebra or a proof of the Brouwer fixed point theorem
Learning Outcomes
1. Understand and use the basic algebra of set theory, including De Morgan's Laws
2. State the definition of a topological space and describe several examples of this concept
3. Explain the relationship between topologies and continuous functions
4. Understand the concept of homeomorphism
5. Construct new topological spaces using the subspace and quotient constructions
6. Understand and explain the concept of compactness, prove some basic theorems relating to this concept
7. Understand and explain the concept of connectedness, prove some basic theorems relating to this concept
8. Apply topological ideas to solve problems in other areas of mathematics or applied mathematics e.g. topological proof of the fundamental theorem of algebra or a proof of the Brouwer fixed point theorem