IntroductionComplexes and Their CohomologyChain Complexes: The Backbone of Homological AlgebraHomology: Measuring the Failure of ExactnessFunctors and Derived FunctorsFunctors: Morphisms Between CategoriesDerived Functors: Lifting Functors to the Homological LevelExact Sequences: The Drama of Homological AlgebraShort Exact Sequences: The Perfect BalanceLong Exact Sequences: Chaining the DramaConclusion
0 Comments
IntroductionNeural Networks: The Building BlocksThe Universal Approximation Theorem: Neural Networks Can Do Anything… AlmostGradient Descent: Rolling DownhillDeep Learning: Going DeeperVanishing and Exploding Gradients: The Perils of DepthRegularization: Keeping the Overfitting Gremlins at BayApplications and Beyond: Where Theory Meets PracticeConvolutional Neural Networks: Image WhisperersRecurrent Neural Networks: Masters of SequenceConclusionIntroductionGraph Theory in Computational BiologyDNA Sequencing: The Eulerian Path ApproachProtein-Protein Interaction Networks: Finding CliquesMetabolic Pathways: Shortest Path ProblemsAdvanced Applications: From Theoretical Insights to Practical UsesGene Regulatory Networks: Cycles and Feedback LoopsPhylogenetic Trees: Constructing Evolutionary HistoriesConclusionIntroductionSymplectic Geometry: The Stage for Hamiltonian DynamicsThe Symplectic Form: Setting the SceneHamiltonian Functions: The ScriptwritersHamiltonian Systems: The PerformersPhase Space: The Dance FloorPerturbation Theory: Dealing with Unruly DancersApplications: From Celestial Mechanics to Quantum PhysicsCelestial Mechanics: The Grand Ballet of the CosmosQuantum Mechanics: The Subatomic WaltzConclusion |
AuthorTheorem: If Gray Carson is a function of time, then his passion for mathematics grows exponentially. Archives
November 2024
|