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Finally, one needs to know that there is not one geometry, but many, and transformation groups are the best way to distinguish between them. Two chapters are devoted to each approach: The? Thus, the? Get A Copy. Hardcover , pages.


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Shining a light on curriculum

Lists with This Book. This book is not yet featured on Listopia. Community Reviews. Showing Rating details. More filters. Sort order. Feb 04, Shaun Zhang rated it liked it Shelves: mathematics.

The Four Pillars of Flipping the Classroom

A good introduction to Eulidean and projective geometry. Nov 05, Michelle rated it really liked it. Helpful for sorting out the differing approaches to undergraduate geometry studies. Michael rated it liked it Jun 16, Carlos Souza rated it it was amazing Feb 14, This is the main reason I decided to write this blog post. Recently, there has been an upsurge in the availability of many easy-to-use machine and deep learning packages such as scikit-learn , Weka , Tensorflow , R-caret etc.

Machine Learning theory is a field that intersects statistical, probabilistic, computer science and algorithmic aspects arising from learning iteratively from data and finding hidden insights which can be used to build intelligent applications. Despite the immense possibilities of Machine and Deep Learning, a thorough mathematical understanding of many of these techniques is necessary for a good grasp of the inner workings of the algorithms and getting good results.

Why Worry About The Maths?

The Pillars of Mathematical Character | AIMS Blog | Maths puzzles, Character education, Math

There are many reasons why the mathematics of Machine Learning is important and I will highlight some of them below:. The main question when trying to understand an interdisciplinary field such as Machine Learning is the amount of maths necessary and the level of maths needed to understand these techniques. The answer to this question is multidimensional and depends on the level and interest of the individual. Research in mathematical formulations and theoretical advancement of Machine Learning is ongoing and some researchers are working on more advance techniques.

The twofold difficulty lies not only in seeing that all of the representations are more-or-less equivalent, but also in picking the best representation for a particular task. This idea extends far beyond pure mathematics. Even a webpage is a representation of other ideas. We can get all semiotic about representation — talking about signified vs. Then we get to abstraction. This idea trips up a lot of students.


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Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line. Things still have meaning when we abstract, but the meanings can be hard to see. Worse yet, symbols can have multiple meanings. But it seems difficult and arbitrary to many students. And what about variables? Yet it can seem very confusing. Confusion sets in! But abstraction is necessary and crucial. Too many unsuccessful students are so concrete that they see only the toads and never the gardens.

Abstraction requires moving from the specific to the general. Even numbers are actually abstract. And then what about fractions?


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  • More abstract still. And negative numbers?? And irrational numbers??? And complex numbers???? Even maps which I mentioned above when discussing representation are truly abstract.