why is linear algebra a 3000 course

MTHS 3000: Linear Algebra Course in Mathematical Sciences Course Description: Understanding concepts from linear algebra is essential to the serious study of many disciplines, ranging from physics and chemistry to economics and computer and data science, not to mention the further study of higher mathematics.

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Is there a 20-hour linear algebra course?

Course Description: Understanding concepts from linear algebra is essential to the serious study of many disciplines, ranging from physics and chemistry to economics and computer and data science, not to mention the further study of higher mathematics. In this course, we'll be looking at both computational and theoretical aspects of linear algebra, as well as at a number of …

Who teaches the linear algebra course?

Course ID: MATH 3000. 3 hours. Course Title: Introduction to Linear Algebra. Course Description: Theory and applications of systems of linear equations, vector spaces, and linear transformations. Fundamental concepts include: linear independence, basis, and dimension; orthogonality, projections, and least squares solutions of inconsistent systems; eigenvalues, …

What are the fundamental concepts of linear algebra?

Linear algebra is often the first course one takes where there is some emphasis on rigorous proofs. Prior courses emphasize calculation by methods that the students are told work. This is not mathematics--it is essentially arithmetic. Thus, in a sense, linear algebra is often the first "real" math course that students ever take.

Why is linear algebra important in engineering?

Answer (1 of 8): After reading through the answers and some of the replies/comments, it seems that the biggest issue is confusion over the fact that High School Algebra and Linear Algebra share the word Algebra as part of the name. So I will, …

Is Linear Algebra The hardest math class?

What grade is linear algebra taught?

Is Linear Algebra harder than Calc?

Why is linear algebra so important?

Is Linear Algebra a college course?

Is Linear Algebra Post AP?

Should I learn calculus before linear algebra?

Is linear algebra pure math?

Do engineers have to take linear algebra?

What is linear algebra used for in real life?

How important is linear algebra in machine learning?

Is linear algebra used in AI?

What is linear algebra?

with matrices and vectors, linear algebra might be defined as the study of objects where addition makes sense and maps between those objects which respect addition. An additive (i.e. linear) structure is one of the most pleasing structures one can have on a mathematical object.

Why is linear algebra so difficult?

I think linear algebra can be difficult for students because it can be a first course involving rigorous proofs. For me, linear algebra was difficult the first time around because I was not serious about academics yet and the course was difficult enough that I couldn't get by without studying.

What is the main point of linear algebra?

One main point of linear algebra is that linear equations are easy to solve. Let me explain.

What is the most application-worthy part of linear algebra?

2) the single most application-worthy part of linear algebra is principal-component analysis, also known as a million other names as every field rediscovers it and puts their own name on it. The toy example I have in my head is when you have a lot of points on a 2-D plot that falls in one line - don't you really want to think of it as a line in one dimension? Congrats, you've discovered 1-d principal component analysis ( or linear regression; I don't think of the two as much different =D).

Why is algebra important?

Algebra is useful because you can leave an expression with the variable intact and solve it for ALL values of that number. This is especially useful when:

Why does geometry fail in R?

Geometry fails. This is partially due to the way it's taught. We like to introduce vectors as real space components, which is great for matrices in R 3, but when you start taking higher dimensional spaces, attempts to visualize cause more problems than they solve.

What is the struggle with algebra?

Students who struggle with Algebra, while succeeding in earlier branches of math, tend to be the ones who struggle with abstraction.

When is linear algebra useful?

It's useful when you have many moving parts in an engine, concentrations of multiple chemicals in a test tube , many regions of atmosphere in a climate simulation, prices of stocks in a market, etc..

Why is linear algebra important?

Because linear equations are so easy to solve, practically every area of modern science contains models where equations are approximated by linear equations (using Taylor expansion arguments) and solving for the system helps the theory develop.

What is the importance of understanding linear algebra?

Understanding the tools of linear algebra gives one the ability to understand those theories better, and some theorems of linear algebra require also an understanding of those theories ; they are linked in many different intrinsic ways.

What are the applications of linear equations?

In the abstract, it allows you to manipulate and understand whole systems of equations with huge numbers of dimensions/variables on paper without any fuss, and solve them computationally. Here are some of the real-world relationships that are governed by linear equations and some of its applications: 1 Load and displacements in structures 2 Compatability in structures 3 Finite element analysis (has Mechanical, Electrical, and Thermodynamic applications) 4 Stress and strain in more than 1-D 5 Mechanical vibrations 6 Current and voltage in LCR circuits 7 Small signals in nonlinear circuits = amplifiers 8 Flow in a network of pipes 9 Control theory (governs how state space systems evolve over time, discrete and continuous) 10 Control theory (Optimal controller can be found using simple linear algebra) 11 Control theory (Model Predictive control is heavily reliant on linear algebra) 12 Computer vision (Used to calibrate camera, stitch together stereo images) 13 Machine learning (Support Vector Machine) 14 Machine learning (Principal component analysis) 15 Lots of optimization techniques rely on linear algebra as soon as the dimensionality starts to increase. 16 Fit an arbitrary polynomial to some data.

What is the motivation to study linear algebra?

Your beginning motivation to study linear algebra is to put together what you initially learn in (mathematically) geometry and calculus and in (education) high school, college, or even first year or second year of university.

What happens if you use only the first two terms of the Taylor expansion of f?

If you use only the first two terms of the Taylor expansion of f, you have a linear approximation to your function f:

What is one application of linear algebra?

One application of Linear Algebra is in the use of eigenvalues.

What is the essence of linear algebra?

At its core, Sanderson’s ‘ Essence of Linear Algebra ’ series seeks to introduce, motivate, and conceptualise many of the basic ideas around linear algebra in terms of linear transformations and their associated visualisations. As it turns out, this is a really helpful way to get your head around many of the core fundamentals.

What is linear transformation?

A linear transformation is a way of changing the shape of a ‘space’ (in this case, the 2D plane), in such a way that: Keeps parallel lines parallel. Maintains an equal distance between parallel lines that were equally spaced to begin with. Leaves the origin at the origin.

What does a 2x2 matrix represent?

We’ve just demonstrated that a 2x2 matrix will necessarily represent some kind of linear transformation in 2D space. In particular, for a given matrix [ [a, b], [c, d]], the vectors [a, c] and [b, d] represent the coordinates of ‘transformed î ’ and ‘transformed ĵ ’ respectively.

How many types of linear transformations are there?

Broadly speaking, this gives us three different types of linear transformations that we could do:

What happens when theoretical foundations are predicated on rote learning and plugging numbers into formulae?

If your theoretical foundations are predicated on rote learning and plugging numbers into formulae, without a deeper appreciation and understanding of what’ s actually going on, then they tend to fall down under the weight of something as heavy as, let’s say, machine learning.

Is linear algebra problematic?

Going from the ‘how’ to the ‘why’. This slightly utilitarian attitude to teaching linear algebra is clearly problematic. Mathematics is a discipline that relies on an ‘incremental’ learning — gaining new knowledge often requires you to build upon what you already know.

Who made 3Blue1Brown?

At this point, I’ll mention that this blog was heavily inspired by a series of videos made by Grant Sanderson (a.k.a. 3Blue1Brown ). For those unfamiliar with his work, Sanderson creates really nicely animated videos in a way that makes complicated mathematical subjects accessible to the educated layman (his videos explaining neural networks and cryptocurrency are well worth your time).