2 Books Make You a Discrete Math Pro

today I would like to share with you two books that I think they can help you in math Foundation courses in computer science first up how to read and do proofs by Daniel solo first highlight in [Applause] tuition okay this is how Professor solo illustrates the process tackling appr proof what how come a maze has anything related to proofs let me show you let's take this classic proposition as an example if the right triangle XYZ with sides of length x and y and hypotenuse of length Z has an area of Z ² over 4 then the triangle XYZ is isos tackling a proof is typically like this you have something at hand and you want to reach out to the destination as well this is just like going from A to B or from B to a what do we have we know that the area of the triangle is Z ² over 4 besides this example we also know that the area of the triangle is BAS multiple height divide by 2 then that would be XY / 2 and is equal to to Z ² / 4 multiply 4 on both side we got something nicer by Pythagorean theorem we also know that s² + y² = z ² use this expression to subtract the previous one we got this it's a perfect square trom meals and we know that it's equivalent to this at this point we somehow don't know where to go you start from a and try and go to B you hasitate what's doing next then you can change your mindset start from B and go backward to a b is what we need to prove that the triangle XYZ is isoceles then by isoceles it means that X = Y from X = Y we have this and square both side we have this when the path is connected it means you can go all the way from the antecedent to the consequent forward a can find B and B can find a that's the forward and backward second highlight reading and doing proof like common English sentence suppose you need to prove this theorem if n is an even number then n square is even you will not write proof like this as it is difficult to understand and way too abstract rather reading your proof is just like reading English sentence elegant like poem every sentence makes sense and nicely related to each other third highlight practical exercise with Solutions in this book Professor solo provides many many exercise to get your hands dirty you can go to the ww. wi.com colge SLS solo for the solutions and lecture videos next let's explore Michael Si's introduction to the theory of computation and his book has online lectures on mitw the goal of this book is to answer one questions what are the fundamental capabilities and limitations of computers to answer this question this book focus on three areas of theory of computations automata and languages computability Theory complexity Theory when you're reading this book Professor sier keep enforcing the big picture of each Topic in the meantime each section has an easy to hard learning curve which provides a great experience let's take the section of nondeterminism finite at as example it starts with the big idea and big picture as we mentioned before so we know that non-determinism final automatan is related to the theory of computation when we start learning a new subject we're not familiar with the term and definition so when I say nondeterminism finite atomm it sounds difficult to understand in English already but professor sier said nondeterminism may be real as a kind of parallel computation where multiple independent processes or threats can be running concurrently oh that's some words I'm familiar with after giving this intuition Professor syus gives a simple example on NFA it looks like throwing a trail of inputs like 01 01 1 0 in parallel and see which one is accepted with intuition and example in mind a formal definition will not be that scary anymore then comes the hardest part the proof of this definition but we always have a proof idea ahead of each proof so you know the skeleton and strategy of the proof I really enjoyed this easy to hard progress that's it I hope you like it I'll see you next time

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Length: 5min 26sec (326 seconds)

Published: Tue Jun 18 2024