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Recommended Courses for Numerical Methods & Linear Algerbra

Recommended Courses for Numerical Methods & Linear Algerbra

Cource List:

1) Introduction to Linear Algebra and Python - Howard University
 

This course is the first of a series that is designed for beginners who want to learn how to apply basic data science concepts to real-world problems. You might be a student who is considering pursuing a career in data science and wanting to learn more, or you might be a business professional who wants to apply some data science principles to your work.

Or, you might simply be a curious, lifelong learner intrigued by the powerful tools that data science and math provides. Regardless of your motivation, we’ll provide you with the support and information you need to get started.

In this course, the fundamentals of linear algebra will be covered , including systems of linear equations, matrix operations, and vector equations. Whether you’ve learned some of these concepts before and are looking for a refresher or you’re brand new to the ideas we’ll cover, you’ll find the materials to support you.
 


2) Fundamental Linear Algebra Concepts with Python  from Howard University

In this course, you'll be learn to finding inverses and matrix algebra using Python. You will also practice using row reduction to solve linear equations as well as practice how to define linear transformations. Get started!

 

3) Introduction to Linear Algebra from The University of Sydney

Linear algebra and calculus are the two most important foundational pillars on which modern mathematics is built. They are studied by almost all mathematics students at university, though typically labelled as different subjects and taught in parallel.

Over time, students discover that linear algebra and calculus are inseparable (but not identical) twins that interlock to form the backbone of almost all applications of mathematics to physical and biological sciences, engineering and computer science. It is recommended that participants in the MOOC Introduction to Linear Algebra have already taken, or take in parallel, the MOOC Introduction to Calculus.

All of our modern technical and electronic systems, such as the internet and search engines, on which we rely and tend to take for granted in our daily lives, work because of methods and techniques adapted from classical linear algebra. The key ideas involve vector and matrix arithmetic as well as clever methods for working around or overcoming difficulties, a form of obstacle avoidance, articulated in this course as the Conjugation Principle.

This course emphasises geometric intuition, gradually introducing abstraction and algebraic and symbolic manipulation, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics. Students taking Introduction to Linear Algebra will:

• gain familiarity with the arithmetic of geometric vectors, which may be thought of as directed line segments that can move about freely in space, and can be combined in different ways, using vector addition, scalar multiplication and two types of multiplication, the dot and cross product, related to projections and orthogonality (first week),

• develop fluency with lines and planes in space, represented by vector and Cartesian equations, and learn how to solve systems of equations, using the method of Gaussian elimination and introduction of parameters, using fields of real numbers and modular arithmetic with respect to a prime number (second week),

• be introduced to and gain familiarity with matrix arithmetic, matrix inverses, the role of elementary matrices and their relationships with matrix inversion and systems of equations, calculations and theory involving determinants (third week),

• be introduced to the theory of eigenvalues and eigenvectors, how they are found or approximated, and their role in diagonalisation of matrices (fourth week),

• see applications to simple Markov processes and stochastic matrices, and an introduction to linear transformations, illustrated using dilation, rotation and reflection matrices (fourth week), • see a brief introduction to the arithmetic of complex numbers and discussion of the Fundamental Theorem of Algebra (fourth week).

4) Linear Algebra: Linear Systems and Matrix Equations from Johns Hopkins University

This is the first course of a three course specialization that introduces the students to the concepts of linear algebra, one of the most important and basic areas of mathematics, with many real-life applications.

This foundational material provides both theory and applications for topics in mathematics, engineering and the sciences. The course content focuses on linear equations, matrix methods, analytical geometry and linear transformations. As well as mastering techniques, students will be exposed to the more abstract ideas of linear algebra. Lectures, readings, quizzes, and a project all help students to master course content and and learn to read, write, and even correct mathematical proofs.

At the end of the course, students will be fluent in the language of linear algebra, learning new definitions and theorems along with examples and counterexamples.

Students will also learn to employ techniques to classify and solve linear systems of equations. This course prepares students to continue their study of linear transformations with the next course in the specialization.

 

5) Advanced Linear Models for Data Science 1: Least Squares from Johns Hopkins University

This class is an introduction to least squares from a linear algebraic and mathematical perspective.
 

Before beginning the class make sure that you have the following: - A basic understanding of linear algebra and multivariate calculus. -

A basic understanding of statistics and regression models. - At least a little familiarity with proof based mathematics. - Basic knowledge of the R programming language.

After taking this course, students will have a firm foundation in a linear algebraic treatment of regression modeling. This will greatly augment applied data scientists' general understanding of regression models.

6) Regression Models from Johns Hopkins University

Linear models, as their name implies, relates an outcome to a set of predictors of interest using linear assumptions.

Regression models, a subset of linear models, are the most important statistical analysis tool in a data scientist’s toolkit.

This course covers regression analysis, least squares and inference using regression models. Special cases of the regression model, ANOVA and ANCOVA will be covered as well. Analysis of residuals and variability will be investigated.

The course will cover modern thinking on model selection and novel uses of regression models including scatterplot smoothing.

 

7) YouTube Videos:
    a) Regression  

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