DEPARTMENT OF PHYSICS AND ASTRONOMY  (202) 8066245 (main office), 5830 (fax)
Advanced Mathematical Methods in Physics 1
PHYS266 [CRN: 82756]: MWF, 3:30  4:20, TKH #103
[Topics ][ Daily
Schedule ][ eGear ][Welcome ]
Component 
Time 
Remark

% of Grade 

Homework 
As assigned in class 
Late HW = 0 credit !!! 
40% 
Term paper 
By the last day of classes 
Topical 
60% 
The aim of the course is to introduce, develop and discuss various methods of determining global characteristic properties of spaces which occur in theoretical and mathematical physics. Throughout the course, the emphasis is on the applications of these results rather than their proofs. The course is to be regarded as an statistically significant sampler rather than a definitive compendium, and students are strongly encouraged to study particular topics mentioned in the course, in detail and depth surpassing the discussions in class; this is the purpose of the term paper.
“Success = 1% inspiration + 99% perspiration”T.A.
Edison
But, learning is still 100% learnig + 0% teaching.
Daytoday schedule: Students are expected to read ahead
08/26: Introductory Matters
08/28: Motivations and introduction to topology: §1.12
08/30: Basic notions in topology: §1.25
09/02: Observed Holiday:
Labor Day
09/04: Exterior algebra: §§1.
09/06: Vectors, frames, differential forms, pullbacks
and exterior derivatives : §§2.16
09/09: Poincaré lemma, de Rham cohomology, integration
and stokes' theorem: §§2.710
09/11: Metric structures: §§3.
09/13: Maxwell's equations, connection/potential, curvature/field
strength: §§4.13
09/16: Exterior covariant derivative, YangMills and
gauge theories: §§4.47
09/18: The equivalence principle, metric connection,
action and field equations: §§5.15
09/20: Energymomentum of matter, Einstein gauge and
the geometry of curvature and torsion: §§5.69
09/23: The Lie derivative: §§6.
09/25: Manifolds, submanifolds, tangent space, and frames:
§§7.17
09/27: Differential forms on manifolds, integration,
metric and gauge theories: §§7.814
09/30: Lie groups, their representations and algebras:
§§ 8.13
10/02: Relations between Lie groups and Lie algebras,
the MaurerCartan form: §§8.46
10/04: The fundamental group, §3.12
10/07: Simplexes, triangulation and calculations: §3.35
10/09: Homology groups and simplexes, abelian groups,
§4.13
10/11: Relative homology groups, exact sequences, and
torsion, Künneth and EulerPoincaré formulas: §4.46
10/14: Observed Holiday:
Columbus Day
10/16: Higher homotopy groups: §5
10/18: De Rham cohomology vs. homology: §6
10/21: Fibre bundles: §7.14
10/23: Sections, singularities, reduction and contraction:
§7.56
10/25: Hamiltonian, almost complex and Gstructures:
§7.78
10/28: Connection, curvature, parallel transport, and
Binachi identities: §7.914
10/30: Tangent bundle, three connections: LeviCivita,
YangMills and Maxwell: §7.520
11/01: Characteristic classes: §7.2126
11/04: Calculation of and with characteristic classes:
§ 7.2730
11/06: Morse inequalities and lemma, §8.12
11/08: Symmetry breaking and equilibira, §8.34
11/11: Topological defects and homotopy theory: §9
11/13: Instantons I: §10.15
11/15: Instantons II: §10.610
11/18: Instantons and twistors, §10.1115
11/20: Instantons and holomorphic vector bundles, monopoles
and the AharonovBohm effect, §10.1620
11/22: Clifford algebras, spinors and the Dirac operator:
§§11.15
11/25: The Dirac action, spin structures and Kähler
fermions, §§11.68
11/27: Anomalies and an algebraic approach to them§§12
.
11/29: Observed Holiday:
Thanksgiving Recess
12/02: Anomalies from perturbative calculations; §§13.
Algebraic geometry crash course:
12/04: Spacetime in string theory, compactification and CalabiYau manifolds.
12/06: Spectral sequences, diagram chasing and group
actions as calculational tools.
Collaboration policy
Collaboration  but not blind copying  on the homework assignments is strongly encouraged; students should use this to learn from each other. However, no collaboration is permitted on the term papers: by signing them, the students implicitly agree to abide by this policy. Violation of this policy is covered under University regulations on academic dishonesty and cheating.
Presentation and organization
While a neat presentation of home, quiz and examwork is not required for full credit, it certainly makes it easier to assess the quality of the work and give the proper credit due. In all cases, include a simple sketch if it might help conveying the approach or the calculations. Where necessary, include all units and symbols such as the measure of an integral, arrow on a vector, vertical bars for the absolute value of a quantity, for the magnitude of a vector or for the determinant of a matrix, etc.
ADA disclaimer
Howard University is committed to providing an educational environment
that is accessible to all students. In accordance with this policy [details],
students in need of accommodations due to a disability should contact the
Office of the Dean for Special Student Services at 2022382420, for verification and determination of reasonable accommodations
as soon as possible after admission to the Law School, or at the beginning
of each semester.
© Tristan Hübsch, 2002