MY-ASSIGNMENTEXPERT™可以为您提供math.wustl Math5052 Functional Analysis信息论课程的代写代考和辅导服务！
这是圣路易斯华盛顿大学泛函分析课程的代写成功案例。
Math5052课程简介
Topics. This will be the second semester of a two semester graduate-level introduction to the theory of measure and integration in abstract and Euclidean spaces. Math 5051 and 5052 form the basis for the Ph.D. qualifying exam in analysis.
Prerequisites. Math 5051, or permission of instructor.
Time. Classes meet Mondays, Wednesdays, and Fridays, 10:00 am to 11:00 am, in Cupples I Hall, room 218.
Text. The lectures will follow the book Real Analysis for Graduate Students, Version 2.1, by Richard F. Bass. ISBN-13: 978-1502514455
This textbook was also used in Math 5051.
Note that, although a PDF version is freely available, the printed version is cheap and handy to have at times when computers are not available.
Prerequisites
Tests. There will be one midterm examination on Wednesday, March 9th, in class.
There will be a cumulative final examination, emphasizing later material, on Friday, May 6th, 2016 at 10:00am-12:00pm in Room 199.
Students may choose to take the real analysis qualifying examination at that date instead, which will last from 10:00am until 1:00pm in the same location.
No electronic devices will be allowed during these tests.
Grading. One grade will be assigned for all homework, one for the midterm, and one for the final examination. These grades will contribute as follows to the course grade: Homework 50%, Midterm 20%, Final 30%. Students taking the Cr/NCr or P/F options will need a grade of D or better to pass.
Math5052 Functional Analysis HELP（EXAM HELP， ONLINE TUTOR）
If $\mathcal{Z}={\ldots,-2,-1,0,1,2, \ldots}$ denotes the set of all integers and $N={1,2,3, \ldots}$ the set of all natural numbers, exhibit the following sets in the form $A={a, b, c, \ldots}$ :
(i) $\left{x \in \mathbb{Z}: x^2-2 x+1=0\right}$
(ii) ${x \in \mathbb{Z}: 4 \leq x \leq 10}$
(iii) $\left{x \in N: x^2<10\right}$
Construct the truth table for De Morgan’s Law:
$$
\sim(p \wedge q) \Leftrightarrow((\sim p) \vee(\sim q))
$$
Construct truth tables to prove the following tautologies:
$$
\begin{aligned}
(p \Rightarrow q) & \Leftrightarrow(\sim q \Rightarrow \sim p) \
\sim(p \Rightarrow q) & \Leftrightarrow p \wedge \sim q
\end{aligned}
$$
Construct truth tables to prove the associative laws in logic:
$$
\begin{aligned}
& p \vee(q \vee r) \Leftrightarrow(p \vee q) \vee r \
& p \wedge(q \wedge r) \Leftrightarrow(p \wedge q) \wedge r
\end{aligned}
$$
Of 100 students polled at a certain university, 40 were enrolled in an engineering course, 50 in a mathematics course, and 64 in a physics course. Of these, only 3 were enrolled in all three subjects, 10 were enrolled only in mathematics and engineering, 35 were enrolled only in physics and mathematics, and 18 were enrolled only in engineering and physics.
(i) How many students were enrolled only in mathematics?
(ii) How many of the students were not enrolled in any of these three subjects?
List all of the subsets of $A={1,2,3,4}$. Note: $A$ and $\emptyset$ are considered to be subsets of $A$.
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