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Study Plan: Spectral Graph Theory & Quantum Walks - Coggle Diagram
Study Plan: Spectral Graph Theory & Quantum Walks
Stage 1 – Year 1: Learn Foundations
---- Spectral Graph Theory
------ Adjacency & Laplacian matrices
------ Eigenvalues & eigenvectors
------ Classical results
---- Algebraic Combinatorics
------ Association schemes
------ Regular and distance-regular graphs
------ Symmetry & eigenvalue properties
------ Classical vs. quantum walks
------ Behavior on small graph families (paths, cycles)
---- Academic Skills
------ Reading papers carefully
------ Attending seminars
------ Presenting small results
---- Basics of Quantum Walks
Stage 2 – Late Year 1 / Early Year 2: Explore Research Directions
---- Literature Review
------ Introductory-level papers recommended by Prof. Tanaka
---- Analyze Small Examples
------ Spectra of small graphs
------ Weighted graph behavior
------ Basic quantum walk behavior
------ Elementary association scheme properties
---- Discussions with Professor Tanaka
------ Clarify concepts
------ Receive feedback
---- Narrow Thesis Topic
------ Choose a feasible, meaningful topic
Stage 3 – Year 2: Conduct Beginner-Level Research
---- Literature Study
------ Focus on definitions, basic lemmas, classical results
---- Attempt Simple Research Problems
------ Spectral properties of weighted or irregular graphs
------ Transition probabilities of simple quantum walks
------ Elementary association scheme analysis
---- Thesis Development
------ Prepare presentations
------ Write and revise drafts under supervision
-- Candidate Research Problems (Examples Only)
---- Spectral properties of weighted irregular graphs
---- Basic quantum walk behavior on small graph families
---- Elementary properties of association schemes
Final Goal
--
- Build strong foundation in algebraic combinatorics & spectral graph theory
---- Complete well-structured master’s thesis
---- Develop mathematical maturity, logical reasoning, academic skills
---- Prepare for future research in discrete mathematics and quantum walks