数学偏微分方程代写 4143/6543代写 偏微分方程代写代写
4754143/6543 Partial Differential Equations 数学偏微分方程代写 All explanations and calculations must be shown in full to receive full credit. You may use the book but no electronic computation d...
View detailsSearch the whole station
数学表达与推理代写 General instructions Please read the following instructions carefully before starting the problem set. They contain important information about
Please read the following instructions carefully before starting the problem set. They contain important information about general problem set expectations, problem set submission instructions, and reminders of course policies.
• Your problem sets are graded on both correctness and clarity of communication. Solutions that are technically correct but poorly written will not receive full marks. Please read over your solutions carefully before submitting them.
• Solutions must be typeset electronically, and submitted as a PDF with the correct filename. Hand-written submissions will receive a grade of ZERO.
The required filename for this problem set is problem set3.pdf.
• Each problem set may be completed in groups of up to three—except for Problem Set 0. If you are working in a group for this problem set, please consult https://github.com/MarkUsProject/ Markus/wiki/Student-Guide for a brief explanation of how to create a group on MarkUs.
If you haven’t used MarkUs before, give yourself plenty of time to figure it out, and ask for help if you need it! If you are working with one or more partner(s), you must form a group on MarkUs, and make one submission per group.
• Your submitted file(s) should not be larger than 5MB. You might exceed this limit if you use a word processor like Microsoft Word to create a PDF; in that case, you should look into PDF compression tools to make your PDF smaller, but please make sure that your PDF is still legible!
• Submissions must be made before the due date on MarkUs. Please see the Assessment section on the course website for details on how late submissions will be handled.
• MarkUs is known to be slow when many students try to submit right before a deadline. Aim to submit your work at least one hour before the deadline. It is your responsibility to meet the deadline. You can submit your work more than once; the most recent version submitted within the deadline (or within the late submission period) is the version that will be marked.
• The work you submit must be that of your group; you may not use or copy from the work of other groups, or external sources like websites or textbooks. Please see the section on Academic Integrity in the course syllabus for further details.
• When doing a proof by induction, always label the step(s) that use the induction hypothesis.
• You may not use forms of induction we have not covered in lecture, except where indicated in the question.
• Please follow the same guidelines as Problem Set 2 for all proofs.
i. Prove that P(2) is true.
Hint: Think about the quantity (x1 + x2)2 − (x1 − x2)2 .
ii. Prove that, for each n ≥ 2, if P(2) and P(n) are true, then P(2n) is also true.
Use this to prove that P(2m) is true for all m ∈ N, where m ≥ 1.
iii. Prove that P(k) ⇒ P(k − 1) for all k ≥ 2. (Hint: Set xk = (x1 + · · · + xk−1)/(k − 1).)
iv. Why is P(n) is true for all n ∈ N, where n ≥ 1? An informal argument here is fine (you do NOT have to provide a rigorous proof).
On Worksheet #10, we looked at representing rational numbers in binary notation. Here, we’ll also consider representations in two other bases that appear often in computer science. Recall that a binary representation of the rational number x is
(a) [3 marks] In each of the following equalities, find the missing representation. To get full credit, you MUST show your work.
i. (EA)16 = (x)8
ii. (755)8 = (x)2
iii. (9009)10 = (x)16
For each part of this question, you may (but are not required to) use any of the following facts.
• Fact 1: ∀n ∈ Z+, n ≤ 2n
• Fact 2: ∀x, y ∈ R≥0 , x ≤ y ⇔ log2(x) ≤ log2(y)
• Fact 3: ∀x, y ∈ R≥0 , x ≤ y ⇔ 2x ≤ 2y
(a) [3 marks] Prove each of the following statements. You do NOT have to use induction on n. (Keep it simple!)
i. n ∈ O(n1+ϵ), for any real number ϵ > 0.
ii. log2(n) ∈ O(n)
iii. 2n ∈ O(n!)
(b) [3 marks] Suppose that f : N → R≥0 , and that
f(n) ∈ O(log2(n)).
Prove that there exists a constant c > 0 such that
2f(n) ∈ O(nc ).
更多代写:cs exam代考 gre作弊后果 英国bio生物学网课代修价格 论文英文字体 如何写abstract 学霸代写
合作平台:essay代写 论文代写 写手招聘 英国留学生代写
4143/6543 Partial Differential Equations 数学偏微分方程代写 All explanations and calculations must be shown in full to receive full credit. You may use the book but no electronic computation d...
View detailsMth 440/540 Homework 计算数论作业代写 (1) Part I a.) Use Mathematica to determine the 100th prime, the 1000th prime, and the 10,000th prime. b.) Use Mathematica to determine the prime (1) ...
View detailsMATH 7241: Problem Set #2 数学课业代做 Reading: relevant background material for these problems can be found in the class notes, and in Ross (Chapters 2,3,5) and in Grinstead and Snell Rea...
View detailsCSC 165 H1 Term Test 3 — Question 1 of 4 计算机科学的数学表达与推理代写 Aids Allowed: Your own notes taken during lectures and office hours, the lecture slides and recordings (for all secti...
View details