Lecture to Vision of Linear Algebra: A New Way to Start Linear Algebra

Lecture to Vision of Linear Algebra: A New Way to Start Linear Algebra
Professor Strang describes independent vectors and the column space of a matrix as a good starting point for learning linear algebra. His outline develops the five shorthand descriptions of key chapters of linear algebra.

#algebra #spring #machinelearning 

 

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Lecture to Vision of Linear Algebra: A New Way to Start Linear Algebra

Lecture to Vision of Linear Algebra: A New Way to Start Linear Algebra

Lecture to Vision of Linear Algebra: A New Way to Start Linear Algebra
Professor Strang describes independent vectors and the column space of a matrix as a good starting point for learning linear algebra. His outline develops the five shorthand descriptions of key chapters of linear algebra.

#algebra #spring #machinelearning 

 

Bailee  Streich

Bailee Streich

1624447260

Course Review: Python for Linear Algebra

Because I am continuously endeavouring to improve my knowledge and skill of the Python programming language, I decided to take some free courses in an attempt to improve upon my knowledge base. I found one such course on linear algebra, which I found on YouTube. I decided to watch the video and undertake the course work because it focused on the Python programming language, something that I wanted to improve my skill in. Youtube video this course review was taken from:- (4) Python for linear algebra (for absolute beginners) — YouTube

The course is for absolute beginners, which is good because I have never studied linear algebra and had no idea what the terms I would be working with were.

Linear algebra is the branch of mathematics concerning linear equations, such as linear maps and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics.

Whilst studying linear algebra, I have learned a few topics that I had not previously known. For example:-

A scalar is simply a number, being an integer or a float. Scalers are convenient in applications that don’t need to be concerned with all the ways that data can be represented in a computer.

A vector is a one dimensional array of numbers. The difference between a vector is that it is mutable, being known as dynamic arrays.

A matrix is similar to a two dimensional rectangular array of data stored in rows and columns. The data stored in the matrix can be strings, numbers, etcetera.

In addition to the basic components of linear algebra, being a scalar, vector and matrix, there are several ways the vectors and matrix can be manipulated to make it suitable for machine learning.

I used Google Colab to code the programming examples and the assignments that were given in the 1 hour 51 minute video. It took a while to get into writing the code of the various subjects that were studied because, as the video stated, it is a course for absolute beginners.

The two main libraries that were used for this course were numpy and matplotlib. Numpy is the library that is used to carry out algebraic operations and matplotlib is used to graphically plot the points that are created in the program.

#numpy #matplotlib #python #linear-algebra #course review: python for linear algebra #linear algebra

Linear Algebra for Data Science: A new way to start — Part 1

Linear Algebra is perhaps one of the most fundamental building blocks for data science, pattern recognition, and machine learning. I believe, understanding fundamentals is the first thing anyone should do before going after advanced topics. Why? Because we don’t want to get stuck in a loop going back and forth in advanced topics and fundamentals!
In this series, I am going to cover topics covered by Prof. Gilbert Strang in his latest lecture series, “A 2020 Vision of Linear Algebra”. It is an excellent lecture series in which he takes a top-down approach in teaching applied linear algebra. My aim here is to share with you my understanding of the topics with relevant details which I believe will aid in understanding the lectures in a better and nuanced way.

#machine-learning #linear-algebra #musings-of-data-science #data-science

Carmen  Grimes

Carmen Grimes

1595494844

How to start an electric scooter facility/fleet in a university campus/IT park

Are you leading an organization that has a large campus, e.g., a large university? You are probably thinking of introducing an electric scooter/bicycle fleet on the campus, and why wouldn’t you?

Introducing micro-mobility in your campus with the help of such a fleet would help the people on the campus significantly. People would save money since they don’t need to use a car for a short distance. Your campus will see a drastic reduction in congestion, moreover, its carbon footprint will reduce.

Micro-mobility is relatively new though and you would need help. You would need to select an appropriate fleet of vehicles. The people on your campus would need to find electric scooters or electric bikes for commuting, and you need to provide a solution for this.

To be more specific, you need a short-term electric bike rental app. With such an app, you will be able to easily offer micro-mobility to the people on the campus. We at Devathon have built Autorent exactly for this.

What does Autorent do and how can it help you? How does it enable you to introduce micro-mobility on your campus? We explain these in this article, however, we will touch upon a few basics first.

Micro-mobility: What it is

micro-mobility

You are probably thinking about micro-mobility relatively recently, aren’t you? A few relevant insights about it could help you to better appreciate its importance.

Micro-mobility is a new trend in transportation, and it uses vehicles that are considerably smaller than cars. Electric scooters (e-scooters) and electric bikes (e-bikes) are the most popular forms of micro-mobility, however, there are also e-unicycles and e-skateboards.

You might have already seen e-scooters, which are kick scooters that come with a motor. Thanks to its motor, an e-scooter can achieve a speed of up to 20 km/h. On the other hand, e-bikes are popular in China and Japan, and they come with a motor, and you can reach a speed of 40 km/h.

You obviously can’t use these vehicles for very long commutes, however, what if you need to travel a short distance? Even if you have a reasonable public transport facility in the city, it might not cover the route you need to take. Take the example of a large university campus. Such a campus is often at a considerable distance from the central business district of the city where it’s located. While public transport facilities may serve the central business district, they wouldn’t serve this large campus. Currently, many people drive their cars even for short distances.

As you know, that brings its own set of challenges. Vehicular traffic adds significantly to pollution, moreover, finding a parking spot can be hard in crowded urban districts.

Well, you can reduce your carbon footprint if you use an electric car. However, electric cars are still new, and many countries are still building the necessary infrastructure for them. Your large campus might not have the necessary infrastructure for them either. Presently, electric cars don’t represent a viable option in most geographies.

As a result, you need to buy and maintain a car even if your commute is short. In addition to dealing with parking problems, you need to spend significantly on your car.

All of these factors have combined to make people sit up and think seriously about cars. Many people are now seriously considering whether a car is really the best option even if they have to commute only a short distance.

This is where micro-mobility enters the picture. When you commute a short distance regularly, e-scooters or e-bikes are viable options. You limit your carbon footprints and you cut costs!

Businesses have seen this shift in thinking, and e-scooter companies like Lime and Bird have entered this field in a big way. They let you rent e-scooters by the minute. On the other hand, start-ups like Jump and Lyft have entered the e-bike market.

Think of your campus now! The people there might need to travel short distances within the campus, and e-scooters can really help them.

How micro-mobility can benefit you

benefits-micromobility

What advantages can you get from micro-mobility? Let’s take a deeper look into this question.

Micro-mobility can offer several advantages to the people on your campus, e.g.:

  • Affordability: Shared e-scooters are cheaper than other mass transportation options. Remember that the people on your campus will use them on a shared basis, and they will pay for their short commutes only. Well, depending on your operating model, you might even let them use shared e-scooters or e-bikes for free!
  • Convenience: Users don’t need to worry about finding parking spots for shared e-scooters since these are small. They can easily travel from point A to point B on your campus with the help of these e-scooters.
  • Environmentally sustainable: Shared e-scooters reduce the carbon footprint, moreover, they decongest the roads. Statistics from the pilot programs in cities like Portland and Denver showimpressive gains around this key aspect.
  • Safety: This one’s obvious, isn’t it? When people on your campus use small e-scooters or e-bikes instead of cars, the problem of overspeeding will disappear. you will see fewer accidents.

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Linear Algebra: The hidden engine of machine learning

Algebra is firstly taken from a book, written by Khwarizmi(780-850 CE), which is about calculation and equations. It is a branch of mathematics in which letters are used instead of numbers. Each letter can represent a specific number in one place, and a completely different number in another. Notations and symbols are also used in algebra to show the relationship between numbers. I remember about 17 years ago when I was an ordinary student in applied mathematics(ordinary graduate today!), I was so curious about some research in algebra, done by Maryam Mirzakhani(1977–2017), at Harvard University about analogous counting problem. This science has evolved a lot throughout history and now includes many branches.

Elementary algebra includes basic operations on four main operations. After defining the signs by which fixed numbers and variables are separated, methods are used to solve the equations. A polynomial is an expression that is the sum of a finite number of non-zero terms, each term consisting of the product of a constant and a finite number of variables raised to whole number powers.

Abstract algebra or modern algebra is a group in the algebra family that studies advanced algebraic structures such as groups, rings, and fields. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Abstract algebra is so popular and used in many fields of mathematics and engineering sciences. For instance, algebraic topology uses algebraic objects to study topologies. The Poincaré conjecture proved in 2003, asserts that the fundamental group of a manifold, which encodes information about connectedness, can be used to determine whether a manifold is a sphere or not. Algebraic number theory studies various number rings that generalize the set of integers.

I believe that the most influencing branch of algebra in other sciences is linear algebra. Let’s suppose that you went out for jogging, that can’t be easy these days with Covid-19 lockdown, and suddenly a beautiful flower catches all your attention. Please don’t be rush and pick it, just take a picture, others can enjoy it, as well. After a while when you look at this picture, you can recognize the flower in the image, because the human brain has evolved over millions of years and able to detect such a thing. We are unaware of the operations that take place in the background of our brains and enable us to recognize the colors in the image, they are trained to do this for us automatically. But, it’s not easy to do such a thing with a machine, that’s why this is one of the most active research areas in machine learning and deep learning. Actually, the fundamental question is: “How does a machine store this image?” You probably know that today’s computers are designed to process only two numbers, 0 and 1. Now, how can an image like this with different features be stored? This is done by storing the pixel intensity in a structure called a “matrix”.

The main topics in linear algebra are vectors and matrices. Vectors are geometric objects that have length and direction. For example, we can mention speed and force, both of which are vector quantities. Each vector is represented by an arrow whose length and direction indicate the size and direction of the vector.

The addition of two or more vectors can be done based on ease of use using parallelogram methods or the method of images in which each vector is decomposed into its components along the coordinate axes. A vector space is a collection of vectors, which may be added together and multiplied by scalars. Scalars generally can be picked up from any field but normally are real numbers.

#matrice #machine-learning #linear-algebra #algebra #deep-learning #deep learning