Systems of ODEs - Saddle Points and Instability
Explore unstable saddle points in 2D linear ODEs, their applications in energy-efficient transport, and analysis using eigenvalues, eigenvectors, and phase portraits.
Eigenvalues and Eigenvectors
Explore eigenvalues and eigenvectors, key concepts in linear algebra. Learn to compute them for any matrix, understand their significance in transformations, and apply them to solve complex linear systems.
More Examples of Second Order Differential Equations
Explore advanced examples of second-order ODEs, including characteristic polynomials, initial conditions, and matrix systems. Learn to solve, plot, and interpret results using MATLAB.
Engineering Math Pre-Req - Quick and Dirty Introduction to Python
High-level introduction to essential Python commands for engineering math, covering arithmetic, loops, arrays, plotting, and solving equations and differential equations.
Engineering Math Pre-Req - Quick and Dirty Introduction to Matlab
High-level introduction to essential Matlab commands for engineering math, covering arithmetic, loops, matrices, plotting, and solving equations and differential equations.
Gentle Introduction to Modeling with Matrices and Vectors - A Probabilistic Weather Model
Explore probabilistic weather modeling using matrices and vectors, with practical examples in Python and MATLAB. Learn to represent and update weather states mathematically.
Learn NumPy in 30 Minutes
Master essential NumPy functions for efficient array operations, data manipulation, and numerical computing in Python. Covers basics to advanced topics like multidimensional arrays, broadcasting, and linear algebra.
Matrix Transpose Isn't Just Swapping Rows and Columns
Explore a unique visualization of matrix transpose, focusing on changing perspective rather than swapping rows and columns. Gain insights into covectors, metric tensors, and adjoints in various fields.
Stability of Forward Euler and Backward Euler Integration Schemes for Differential Equations
Explore stability of Forward and Backward Euler integration schemes for differential equations through eigenvalue analysis, covering continuous and discrete dynamics, scalar and matrix systems.
Introduction to Interpretable Machine Learning - Cynthia Rudin
Explore interpretable machine learning with Cynthia Rudin, covering classification, natural language processing, and decision trees. Gain insights into model complexity and information theory applications.
Linear Spaces of Matrices - Avi Wigderson
Explore linear spaces of matrices with Avi Wigderson, covering motivations, structural results, algorithms, and open problems in mathematics and computer science.
Representation Theory & Combinatorics of the Symmetry Group and Related Structures - Monica Vazirani
Explore symmetry group representation theory and combinatorics, focusing on cycle notation, permutations, and linearization techniques for advanced mathematical analysis.
On Chen’s Recent Breakthrough on the Kannan-Lovasz-Simonovits Conjecture and Bourgain's Slicing Problem - Part III
Explore Chen's breakthrough on the KLS conjecture and Bourgain's slicing problem, covering key mathematical concepts, historical context, and implications for discrete mathematics and computer science.
Sparse Matrices in Sparse Analysis - Anna Gilbert
Explore sparse matrices in compressive sensing, focusing on expander graphs and their applications. Learn about metric repair scenarios and algorithms for sparse signal recovery.
X-Ramanujan Graphs - Ex Uno Plures
Explore X-Ramanujan graphs with Ryan O'Donnell, covering additive lifts, generic graphs, eigenvalues, and matching polynomials in this advanced computer science and discrete mathematics seminar.
Representations of P-Adic Groups - Jessica Fintzen
Explore p-adic group representations, their key questions, and concepts like Moy-Prasad filtration and stable vectors in this advanced mathematics seminar by Jessica Fintzen.
LoRA - Low Rank Adaptation for Parameter Efficient Fine-Tuning
Dive into parameter-efficient fine-tuning with LoRA, exploring low-rank matrices, adapters, and techniques to optimize neural network storage and performance while maintaining accuracy.
Improving the Life-Cycle of Tensor Algorithm Development with ITensors
Explore advanced tensor algorithm development in Julia, focusing on generic programming strategies for efficient computation across CPU, GPU, and QPU architectures using the ITensors framework.
Mathematik für Ingenieure 3
Umfassende Einführung in mehrdimensionale Integration und Vektoranalysis für Ingenieure, mit Fokus auf praktische Anwendungen und Problemlösungen in der höheren Mathematik.
Determinanten
Umfassende Einführung in Determinanten: Definition, Berechnung in 2D, Volumeninterpretation, Leibniz-Formel und Laplace-Entwicklung mit praktischen Beispielen.
Linear Algebra
Umfassende Einführung in die lineare Algebra mit Schwerpunkt auf Matrizen, Determinanten, Eigenwerte und komplexe Zahlen. Praktische Anwendungen und Übungen vertiefen das Verständnis.