00TD02A_Repos - itnett/FTD02H-N GitHub Wiki

Here is an overview of some notable GitHub repositories related to algebra:

  1. The Art of Linear Algebra by kenjihiranabe:

  2. Numerical Linear Algebra by fastai:

    • This repository accompanies the fast.ai Computational Linear Algebra course, offering a free online textbook of Jupyter notebooks. It covers various topics such as matrix decompositions, SVD, PCA, and more, alongside a playlist of lecture videos on YouTube【7†source】.https://github.com/fastai/numerical-linear-algebra

  3. SymPy:

    • SymPy is a comprehensive computer algebra system written in pure Python. It focuses on providing symbolic computation capabilities and is widely used in the scientific Python ecosystem. The repository includes detailed documentation, installation guides, and contribution guidelines【8†source】.https://github.com/sympy/sympy

  4. nalgebra by dimforge:

    • This is a linear algebra library for the Rust programming language. It provides various mathematical structures and operations, including vectors, matrices, and transformations, optimized for performance and ease of use【9†source】.https://github.com/dimforge/nalgebra

  5. galgebra by pygae:

    • This repository offers a symbolic geometric algebra and calculus package for SymPy. It supports enhanced console and LaTeX printing, making it useful for both computational and educational purposes. The repository includes installation instructions and extensive documentation【10†source】.https://github.com/pygae/galgebra

These repositories provide a range of resources for learning and applying algebra in different programming environments and for various applications, from theoretical understanding to practical computational tools.

Here are some useful GitHub repositories related to various mathematical concepts, including arithmetic rules, fractions, percentages, powers, standard form, and factoring:

  1. Math.js:

    • Description: Math.js is a comprehensive math library for JavaScript and Node.js, supporting various data types such as numbers, big numbers, fractions, complex numbers, and more. It includes functions for arithmetic operations, symbolic computation, and more.
    • Features: Fractions, percentages, powers, standard form, and various other mathematical operations.
    • Link: Math.js on GitHub【16†source】.

  2. MathExtended.Fractions:

    • Description: This C# library provides extensive functionality for working with fractions, including addition, subtraction, multiplication, division, and continued fractions.
    • Features: Detailed operations on fractions, making it easier to perform arithmetic and other manipulations.
    • Link: MathExtended.Fractions on GitHub【17†source】.

  3. Khan Academy Math Resources:

    • Description: Khan Academy provides extensive educational content on fractions, decimals, percentages, ratios, and proportions. Their resources include tutorials, practice problems, and quizzes.
    • Features: Converting between fractions, decimals, and percentages; solving percentage problems; factoring quadratics.
    • Link: Fractions, Decimals, & Percentages on Khan Academy【18†source】【19†source】【20†source】.

These resources should help you explore and understand various mathematical concepts, including arithmetic rules, fractions, percentages, powers, standard form, and factoring. Each repository offers unique tools and educational content to enhance your learning and application of these mathematical principles.

Here are some useful GitHub repositories and educational resources for learning about solving equations, systems of equations, and transforming formulas:

Solving Equations

  1. NLsolve.jl:

    • Description: This Julia package solves systems of nonlinear equations. It supports automatic differentiation and provides tools for computing Jacobians and residuals efficiently.
    • Usage: It is particularly useful for complex systems where analytical solutions are difficult to find.
    • Link: NLsolve.jl on GitHub.

  2. Mathematical Python:

    • Description: This resource provides practical examples of solving systems of equations using Python, particularly with scipy.integrate.odeint for differential equations.
    • Usage: Includes examples such as solving mass-spring-damper systems and second-order differential equations.
    • Link: Mathematical Python【27†source】.

Solving Systems of Equations

  1. Khan Academy:

    • Description: Offers comprehensive tutorials and practice exercises on solving systems of equations using methods such as substitution and elimination.
    • Usage: Ideal for step-by-step learning and practice with immediate feedback.
    • Link: Systems of Equations on Khan Academy【28†source】.

  2. Magoosh GRE:

    • Description: Provides detailed explanations and strategies for solving systems of equations, focusing on substitution and elimination methods.
    • Usage: Useful for preparing for standardized tests and reinforcing algebraic problem-solving skills.
    • Link: Magoosh GRE【29†source】.

Transforming and Rearranging Formulas

  1. Math.js:
    • Description: A versatile JavaScript library that supports a wide range of mathematical operations, including transforming and rearranging formulas.
    • Usage: Can be used in both Node.js and browser environments, making it a powerful tool for web-based mathematical computations.
    • Link: Math.js on GitHub【16†source】.

These resources cover a range of topics from basic algebraic operations to more advanced problem-solving techniques, providing both theoretical knowledge and practical tools.

Here are some useful resources for learning about trigonometry and geometry, covering topics such as area, perimeter, volume, surface area, the Pythagorean theorem, trigonometry in right-angled triangles, and vectors in the plane:

1. Basic Geometry and Measurement

Resource: Khan Academy

  • Description: This course covers the basics of geometry, including area, perimeter, volume, and surface area of various shapes. It also delves into the Pythagorean theorem, its applications, and problems involving triangles and other geometric shapes.
  • Link: Basic Geometry on Khan Academy

2. Area, Perimeter, Surface Area, and Volume

Resource: Pass the GED

  • Description: Provides detailed tutorials and practice problems on finding the area and perimeter of 2D shapes and the volume and surface area of 3D shapes. It includes exercises similar to those found on the GED.
  • Link: Pass the GED - Geometry

3. Pythagorean Theorem

Resource: Khan Academy

  • Description: Explains the Pythagorean theorem, how to use it to find side lengths in right triangles, and how to apply it to real-world problems. It also covers using the theorem to find areas and solve word problems.
  • Link: Pythagorean Theorem on Khan Academy

4. Trigonometry in Right-Angled Triangles

Resource: Khan Academy

5. Vectors in the Plane

Resource: Patrick Walls - Mathematical Python

  • Description: Provides a comprehensive guide to understanding vectors, including operations such as addition, subtraction, and scalar multiplication. It also covers more advanced topics like dot products and vector applications in physics and engineering.
  • Link: Vectors in the Plane

These resources should help you master the fundamental concepts of trigonometry and geometry, from basic calculations of area and volume to more complex applications involving vectors and the Pythagorean theorem.

Here are some useful GitHub repositories and educational resources for learning about functions, including linear functions, polynomial functions, exponential functions, polynomial derivatives, and regression:

1. Linear Functions

  • Resource: In Depth: Linear Regression | Python Data Science Handbook
    • Description: This resource covers linear regression in depth, including how to implement it using Python libraries such as Scikit-Learn. It also discusses overfitting, regularization, and visualization of regression results.

2. Polynomial Functions

  • Resource: GitHub - AlexanderSouthan/pyDataFitting

    • Description: This repository provides functions for linear and polynomial regression, including piecewise polynomial fits and constrained polynomial fits. It is designed to offer additional, specialized regression methods beyond what is available in standard libraries like NumPy and SciPy.

  • Resource: GitHub - sigvaldm/localreg

    • Description: This repository focuses on local polynomial regression, which can be useful for smoothing data and dealing with non-linear relationships. It includes examples of both linear and quadratic regression applied locally to data.

3. Exponential Functions

  • Resource: GitHub - Tom-Alexander/regression-js
    • Description: This JavaScript library includes methods for fitting various types of regression models, including exponential functions. It can be used in both Node.js and browser environments and offers configuration options for precision and model parameters.

4. Polynomial Derivatives

  • Resource: Brilliant Math & Science - Derivatives of Polynomials
    • Description: This resource explains how to derive polynomials using the power rule and other basic calculus techniques. It is a useful reference for understanding the fundamental concepts behind polynomial derivatives.

5. Regression with Digital Tools

  • Resource: In Depth: Linear Regression | Python Data Science Handbook

    • Description: In addition to linear regression, this resource covers polynomial regression and ridge and lasso regularization, providing practical examples and code snippets for implementing these techniques in Python.

  • Resource: GitHub - AlexanderSouthan/pyDataFitting

    • Description: This repository includes tools for both linear and polynomial regression, making it a versatile resource for performing regression analysis using Python. It also supports advanced features like constraints and piecewise regression.

These resources provide a comprehensive set of tools and tutorials for understanding and applying various mathematical functions and regression techniques using both theoretical and practical approaches.

GitHub Repositories and Resources for Introductory Physics Topics

1. SI Units and Metric Prefixes

  • Pint: This Python package allows you to define, operate, and manipulate physical quantities with comprehensive support for SI units and metric prefixes. It includes a robust unit conversion system and integration with NumPy for advanced mathematical operations.

  • Units: A C++ library providing compile-time dimensional analysis and unit conversion. It ensures type safety and supports SI units and metric prefixes.

  • Metric: A C# library for working with SI units, offering type-safe operations and conversions between various metric prefixes.

2. Mass, Weight, and Density

  • SI: Another C++ library that offers strong type safety for physical units, including operations and conversions for mass, weight, and density using SI units.

  • KotUniL: A Kotlin library for working with SI units, providing functionality for mass, weight, and density calculations with type safety and compatibility with other Kotlin projects.

3. Uncertainty and Significant Figures

  • Pint: This Python package also supports operations with uncertainty and significant figures, making it a valuable tool for precise scientific calculations.

These repositories and resources provide comprehensive tools and libraries for working with fundamental concepts in physics, including SI units, metric prefixes, mass, weight, density, and uncertainty. They ensure type safety and facilitate complex calculations, making them ideal for educational and professional use in physics and engineering.

GitHub Repositories and Resources for Newton's Laws and Equations of Motion

1. Newton's Laws of Motion

  • Numerical Simulation of Projectile Motion:

    • Description: This repository uses the Euler method to simulate projectile motion, including the effects of gravity and air resistance. It covers Newton's laws and provides numerical methods to explore trajectories and dynamics.
    • Link: Numerical Simulation of Projectile Motion on GitHub

  • Verlet Integrator:

    • Description: This project implements the Verlet integrator to simulate motion under Newton's laws, focusing on stability and accuracy. It includes examples of calculating forces, velocities, and positions with constant acceleration.
    • Link: Verlet Integrator on GitHub

2. Equations of Motion with Constant Speed and Acceleration

These resources provide both theoretical foundations and practical tools for understanding and applying Newton's laws and equations of motion in physics. They include detailed explanations, numerical methods, and simulations to enhance your learning and application of these fundamental concepts.

GitHub Repositories and Resources for Energy Concepts in Physics

1. Work, Power, and Efficiency

  • Work, Energy, and Power:
    • Description: Covers the fundamental concepts of work, power, and efficiency, including calculations and practical examples. It emphasizes the work-energy theorem and provides a solid foundation for understanding these concepts.
    • Link: Work, Energy, and Power on Brown University

2. Kinetic and Potential Energy

  • Numerical Simulation of Projectile Motion:
    • Description: Uses numerical methods to simulate projectile motion, covering kinetic and potential energy calculations. The repository provides practical examples and detailed explanations of energy transformations.
    • Link: Numerical Simulation of Projectile Motion on GitHub

3. Energy Conservation

  • Conservation of Energy in Mechanical Systems:
    • Description: Discusses the principles of energy conservation in mechanical systems, using examples such as vehicle dynamics and wind turbine power generation. It provides practical insights into how energy conservation is applied in real-world scenarios.
    • Link: Conservation of Energy on Brown University

4. First Law of Thermodynamics

  • First Law of Thermodynamics - OpenStax:

    • Description: Provides a comprehensive overview of the first law of thermodynamics, emphasizing the conservation of energy principle applied to thermal systems. It explains how heat and work contribute to the change in internal energy of a system.
    • Link: First Law of Thermodynamics on OpenStax

  • Thermodynamics - MATLAB Central:

    • Description: Explores various forms of energy and their transformations, emphasizing the first law of thermodynamics and its applications. It includes practical examples and scripts for analyzing thermodynamic systems.
    • Link: Thermodynamics on MATLAB Central

These resources provide a comprehensive understanding of energy-related concepts in physics, from basic calculations of work and power to advanced applications of the first law of thermodynamics. They include theoretical explanations, practical examples, and numerical simulations to enhance your learning experience.

Resources for Various Physics and Mathematics Topics

1. Briggs Logarithms

  • Resource: Awesome Math - Logarithms
    • Description: A curated list of resources covering various mathematical topics including logarithms, providing foundational knowledge and applications.

2. Combinatorics

  • Resource: Paths of Combinatorics and Probability

    • Description: Explores the fundamental principles of combinatorics and their application in probability theory, including permutations, combinations, and binomial coefficients.

  • Resource: Khan Academy - Probability and Combinatorics

    • Description: Offers tutorials and practice exercises on combinatorics and probability, helping to build a strong foundation in these areas.

3. Probability and Statistics

  • Resource: Khan Academy - Probability and Statistics
    • Description: Comprehensive lessons on probability, statistical distributions, and data analysis, including quizzes and practice problems to reinforce learning.

4. Phases and Phase Transitions

5. Heat and Internal Energy

6. Second Law of Thermodynamics

  • Resource: The Second Law of Thermodynamics
    • Description: Khan Academy video and articles that provide a thorough explanation of the second law of thermodynamics, its implications, and practical applications.

7. Heat Capacity and Calorimetry

  • Resource: Thermodynamics - Heat Capacity and Calorimetry
    • Description: Detailed exploration of heat capacity, specific heat, and calorimetry, including their mathematical formulations and applications in various physical processes.

8. Number Systems (Binary, Decimal, Hexadecimal)

  • Resource: Khan Academy - Number Systems
    • Description: Lessons and practice exercises on different number systems, including binary, decimal, and hexadecimal, which are crucial for understanding computer science and digital electronics.

9. Algorithmic Thinking and Boolean Algebra

  • Resource: Coursera - Algorithmic Toolbox
    • Description: Repository with solutions and examples from the Algorithmic Toolbox course, covering fundamental algorithms, algorithmic thinking, and boolean algebra.

These resources provide comprehensive coverage of various important topics in physics and mathematics, from basic principles to advanced applications. They include theoretical explanations, practical examples, and interactive exercises to enhance understanding and learning.