Introduction to Robotics
Introduction to Robotics (CS223A) covers topics such as Spatial Descriptions, Forward Kinematics, Inverse Kinematics, Jacobians, Dynamics, Motion Planning and Trajectory Generation, Position and Force Control, and Manipulator Design.
Robustly Transitive Endomorphisms and Strong Volume Expansion for Toral Endomorphisms
Dive into robust transitivity criteria for partially hyperbolic endomorphisms on the two-torus, exploring Blichfedt's theorem and its applications in dynamical systems.
Double and Triple Integrals
Explore double and triple integrals, including polar and spherical coordinates, with practical examples like calculating volumes and solving complex mathematical problems.
Partial Differentiation
Comprehensive exploration of partial differentiation techniques, covering Euler's theorem, Jacobians, envelopes, and evolutes. Includes examples, solutions, and applications in multivariable calculus.
Machine Learning
Explore machine learning models through hands-on tutorials in Python and Julia, covering clustering, regression, neural networks, and more. Practical examples with code provided.
Modern Linear Algebra Using Python Instead of a Textbook
Explore linear algebra concepts through hands-on Python programming, covering matrix operations, decompositions, and applications in machine learning and data analysis.
Differential Calculus for B.Sc. and Engineering Students
Comprehensive coverage of differential calculus topics for BSc and engineering students, including asymptotes, curve tracing, maxima and minima, partial differentiation, and infinite series.
Calculus 3 - How to Change Variables in Multiple Integrals Using the Jacobian
Learn to use the Jacobian for variable changes in multiple integrals, including finding transformations and applying substitutions in advanced calculus problems.
Complex Integration, Cauchy and Residue Theorems - Essence of Complex Analysis
Explore complex integration, Cauchy's theorem, and the residue theorem in this intuitive explanation using Pólya vector field. Gain insights into key concepts of complex analysis.
Oxford Calculus - Jacobians Explained
Comprehensive explanation of Jacobians in 2D coordinate changes, focusing on polar coordinates. Includes derivation of general formula and practical applications with interactive exercises.
On the Classification of Compactified Jacobians of Nodal Curves
Explore modular degenerations of Jacobians when smooth curves become nodal, with insights from recent Pagani-Tommasi findings in algebraic geometry.
Billiards, Arithmetic and Hodge Theory
Explore connections between billiard paths, cusps, curves, heights, and spectral gaps in polygons, encountering chaos and decidability issues in 7 and 12-sided shapes.
Endomorphism Algebras of Geometrically Split Genus 2 Jacobians over Q
Explore endomorphism algebras of geometrically split genus 2 jacobians over Q in this advanced mathematics talk by Francesc Fité, delving into complex algebraic geometry concepts.
Reddening Sequences for Cluster Algebras
Explore reddening sequences in cluster algebras, their implications, and known cases, delving into finite dimensionality, invariants, and canonical bases.
Rigidity and Uniformity in Algebraic Dynamics
Explore connections between algebraic dynamics and arithmetic geometry, focusing on preperiodic points and torsion points in abelian varieties. Learn about recent breakthroughs in uniform bounds and conjectures.
Spectrum of the Ising Model
Explore the correspondence between Ising models and algebro-geometric data, extending Kenyon and Okounkov's work on dimer models and Harnack curves in this advanced mathematical presentation.