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# Course Notes

I will upload (and update) the course notes that I have taken so far. Feel free to contact me if you discover any error or typos.Any courses having the PMATH or the QIC heading were taken at the University of Waterloo; any courses having the MATH heading ﹣ unless otherwise specified ﹣ were taken at Dalhousie University. Any courses having the AARMS heading were offered by AARMS Summer School 2019, whick took place at the University of Prince Edward Island.

*If you are specifically interested in materials relevant to Dalhousie's comprehensive exams, click here to access the solutions to some past comprehensive exams, and the notes covering the comprehensive exam syllabi (number theory and algebra only).*## Number theory courses

### Topics courses

- (AARMS Summer School 2019) AARMS 5910: $q$-series in number theory and combinatorics⁊
- (Winter 2016) PMATH 940: Computational algebraic number theory
- (Fall 2015) PMATH 940: Heights and arithmetic
- (Fall 2014) PMATH 940: $p$-adic analysis

### Other number theory courses

- (Fall 2015) PMATH 740: Analytic number theory
- (Winter 2015+Spring 2016) PMATH 641: Algebraic number theory*

## For Dalhousie non-specialist comprehensive exams

- (Winter 2019) MATH 5045: Advanced Algebra I (module theory; for the algebra comprehensive exam)†§
- (Winter 2019) MATH 5020: Analytic Function Theory (complex analysis) [audited]
- (
*Winter 2019*) MATH RI: Rings and Ideals (for the algebra comprehensive exam; all the concepts are covered. Only left to complete: proofs of the propositions from past comprehensive exams) - (Fall 2018) MATH 5055: Advanced Algebra II (Galois theory; for the algebra non-specialist comprehensive exam)†
- (Fall 2018) MATH 5370: Combinatorics (for the combinatorics non-specialist comprehensive exam)‡§§
- (
*Fall 2018*) MATH GRT: Group Theory (for the algebra comprehensive exam) - (
*Summer 2019*) MATH CGT: Catalan Numbers and Graph Theory (for the combinatorics comprehensive exam; not covered in MATH 5370)

## Other courses taken

- (AARMS Summer School 2019) AARMS 5910: $q$-series in analysis⁊
- (AARMS Summer School 2019) AARMS 5920: Fractals: using iterated function systems (IFS) to construct, explore, and understand fractals
- (Winter 2016) QIC 890: Quantum entanglement and quantum nonlocality**
- (Winter 2015) PMATH 646: Introduction to commutative algebra
- (Winter 2015) PMATH 763: Introduction to Lie groups and Lie algebras
- (Fall 2014) PMATH 945: Dynamical Mordell-Lang Conjecture/Arithmetic Dynamics
- (Fall 2014) PMATH 745: Representation theory of finite groups
- (Fall 2011) MATH 101: Graduate Algebra I
**(D)**

## Current Courses (Fall 2019 onward)

- I have completed the course requirement. Outside of updating the past notes, no new lecture notes will be posted unless I am auditing a course (very unlikely).

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Last modified on 26 July 2019