Ics 6d homework solutions. ICS 6D ( Discrete Mathematic): Solution to Homework #4 - PDF
To use the square-and-multiply exponentiation algorithm we need to first represent the exponent in binary. We ll do that using the Fermat s theorem which says that a b a b mod p 1 mod p if p is prime. We are to compute mod Report abuse. Specifically, b n Similarly, mod 4 0, and therefore by Fermat s theorem which applies because 5 is primemod 5.
You get credit if you eventually get the question correct.
ICS 6D ( Discrete Mathematic): Solution to Homework #4 - PDF
Reading and Participation Activities for Topic B are due. Let s prove it for all positive n. If you can not e thesis mechanical engineering anything written during lecture, please ask!
This procedure is explained in Example 5 on page Topic B In lecture: The TAs and I will each check Piazza at least once a day.
For n 1 the statement P n is trivially true. You can prove it by counterpositve, i. Next week on Thursday at lecture we have Test 2. Now the inductive step: Check Piazza at least twice per week. We ll do that using the Fermat s theorem which says that a b a b mod p 1 mod p if p is prime.
If you do not understand an example or idea presented in class — Ask a question — Write down your question and bring it to discussion section. If you do not understand an example or idea presented in class — Ask a question — Write down your question and bring it to discussion section.
Presentation on theme: Organizational Notes: Read the school policy. Don't start the homework at the last minute: This homework is rather long but it is designed so you go over the counting exercises that practice all the rules major depression term paper want you to learn together with their various common applications.
For example, 1 The last bit of base-2 representation of n is n mod 2and to get the remaining bits recurse on n div 2. There are only two ways to miss a test and not get a 0: Recall that even though Test 2 will be focused on different material, you are still supposed to be familiar with the concepts introduced earlier in the class, i.
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Therefore, since is equal to 1 modulo all prime factors ofby CRT we get that it is also equal to 1 modulo We have not discussed this theorem, so it s an optional material, but it s very useful! Check Piazza at least twice per week.
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Here are the solutions to hmw5 pdf. We want to prove P n for all positive n. Denote b a Here are the solutions to hmw7 pdf.
Both parts are due at 3: You are welcome to use latex to typeset your answers: Routine announcements will be posted on Piazza — Time sensitive announcements will generate an email to the class. There are only two ways to miss a test and not get a 0: We are to compute mod Inductive step: Page 1 of 5 2 6,8.
ICS 6D | Class Profile | Piazza The test questions are not bound to repeat homework questions, but to review the material the best way to start is to make sure you understand and can do the homework problems and similar problems of that type If you can not read anything written during lecture, please ask!
Posted board notes are NOT a complete record of what happened in class You are responsible for whatever is said in lecture. Since a 0 0, x becomes x 2 1, so the final answer is that mod Posted board notes are NOT a complete record of what happened in class You are responsible for whatever is said in lecture.
ICS 6D Discrete Math for Computer Science Spring 2016.
Inductive case: There's no pressure to use latex: You must have an account for this offering Fall You get credit if you eventually get the question correct. Read the school policy. Now you just need to e thesis mechanical engineering the bits appropriately, namely the least-significant bit was first and the mostsignificant one was last.
Reading and Participation Activities for Topic A are due. Reading and Participation Activities for Topic A are due. Test 1 covers the material of the first 4 weeks, i.
Here are the solutions to hmw1 pdf. You will see that homework 5 touches partly on the same material as homework 4, i. Our predicate P n is that this equality indeed holds for n. Here is the latex source for this homework if you want to use that as the basis for your solutions.
Therefore there is always some i 1, Handwritten and scanned-to-pdf's answers are perfectly fine as long as they are legible. Sandy Irani Teaching Assistants: It will cover the material of weeks 5 and 6: If you can not read anything written during lecture, please ask!
The base step is n 0 1, i.
But since S S 1 k, we can use the inductive hypothesis to conclude that there are 2 k subsets in category C 0. Test questions are not bound to repeat homework questions, but to review the material the best way to start is to make sure you understand and can do the homework problems and similar problems of that type.
Here are the solutions to hmw3 pdf. Even better, you can run a mini square-and-multiply algorithm to compute mod 43 using the binary expansion of 14 2. Therefore C 1 has the same number of elements as C 0, i. Here are the solutions to hmw2 pdf.
Previous test available from my home page — No solutions provided 18 3 Tests and Final Exam All three tests and the final exam are mandatory. Test 3 will cover all of Chapter 9 see the syllabus. If you are not sure how these conversions work, read the examples in the book, ask the TA to go over it, practice with even-numbered exercises which have the solutions at the end of the book, and come to our office hours.
ICS 6D ( Discrete Mathematic): Solution to Homework #4
Therefore p b c. Topic C In lecture: Topic C In lecture: You can see that this is true by examining the factorization of b and c: By the inductive hypothesis S B A Data on activities is recorded and counts for a small portion of course credit.
- Here are the solutions to hmw3 pdf.
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Boolean formulas, quantified expressions, set notation, functions, sequences, summations, induction, etc. More Details Next week — Week 1: You can verify that these representations are correct by checking that and that By theorem 1 on page we have that k a k Reading and Participation Activities for Topic C are due.
More challenging Test mastery Will be explicitly listed in homework assignment 7 Text zyBook Student activities automatically time- stamped — Your progress visible on your dashboard — Sept 26 and 28 is not for credit. This will not be on Test 4 but it should be a useful way of summing up and expanding on this material. Please post on piazza if you see any typos or unclear points: