3
1
7530
Please contact MATHSadmin@maths.anu.edu.au for consent to enrol in this course.
true
MATH6204
<p class="MsoNormal"><span>Algebraic topology studies properties of topological spaces and maps between them by associating algebraic invariants (fundamental groups, homology groups, cohomology groups) to each space. </span></p><p class="MsoNormal"><span>This course gives a solid introduction to fundamental ideas and results that are employed nowadays in most areas of mathematics, theoretical physics and computer science. </span></p><p class="MsoNormal"><span>This course aims to understand some fundamental ideas in algebraic topology; to apply discrete, algebraic methods to solve topological problems; to develop some intuition for how algebraic topology relates to concrete topological problems.</span></p><p class="MsoNormal"><span>Topics to be covered include: </span></p><ul><li><div class="MsoNormal"><span>Fundamental group and covering spaces</span></div></li><li><div class="MsoNormal"><span>Brouwer fixed point theorem</span></div></li><li><div class="MsoNormal"><span>Fundamental theorem of algebra</span></div></li><li><div class="MsoNormal"><span>Homology theory and cohomology theory</span></div></li><li><div class="MsoNormal"><span>Jordan-Brouwer separation theorem</span></div></li><li><div class="MsoNormal"><span>Lefschetz fixed theorem</span></div></li><li><div class="MsoNormal"><span>Additional topics (Orientation, Poincare duality, if time permits)</span></div></li></ul><p class="MsoNormal"><span><span>Note: Graduate students attend joint classes with undergraduates but will be assessed separately.</span></span></p><p> </p>
Bachelor degree; with third year Mathematics.
1
false
12651
<p>Assessment will be based on:</p><ul><li>Assignment 1 (10%: LO 1-4)</li><li>Assignment 2 (10%; LO 1-4)</li><li>Assignment 3 (10%; LO 1-4)</li><li>Presentation (10%; LO 1-4)</li><li>Final exam (60%; LO 1-4)</li></ul>
1
1
<p>On satisfying the requirements of this course, students will have the knowledge and skills to:</p>1. Explain the fundamental concepts of algebraic topology and their role in modern mathematics and applied contexts.<br />2. Demonstrate accurate and efficient use of algebraic topology techniques.<br />3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from algebraic topology.<br />4. Apply problem-solving using algebraic topology techniques applied to diverse situations in physics, engineering and other mathematical contexts.
0
Algebraic Topology
6
6
6
Third year Mathematics is required.
Algebraic Topology
Band 2 NP
Mathematics
36 lectures and 10 tutorials.
2010