MY-ASSIGNMENTEXPERT™可以为您提供my.uq.edu.au MATH1061 Discrete Mathematics离散数学课程的代写代考和辅导服务！
这是昆士兰大学离散数学课程的代写成功案例。
MATH1061课程简介
Course Description: Propositional & predicate logic, valid arguments, methods of proof. Elementary set theory. Elementary graph theory. Relations & functions. Induction & recursive definitions. Counting methods pigeonhole, inclusion/exclusion. Introductory probability. Binary operations, groups, fields. Applications of finite fields. Elementary number theory.
There is no particular assumed background, apart from a level of mathematical sophistication roughly equivalent to completion of Queensland Mathematical Methods (formerly Maths B) at high school or MATH1040. Concurrent enrolment in MATH1061 and MATH1040 is appropriate for students who do not have Mathematical Methods from high school but who have a strong mathematical background, however this will require you to do extra work in MATH1061.
Prerequisites
This course provides an introduction to discrete mathematics. It is likely to be useful for students who are planning on studying more mathematics, those intending to teach, and also for those enrolled in computer science, engineering, science and information technology.
Course Changes in Response to Previous Student Feedback
This is an active learning course. Learning resources have been updated and extended.
MATH1061 Discrete Mathematics HELP（EXAM HELP， ONLINE TUTOR）
Given a quadratic equation $a x^2+b x+c=0$ where $x$ is an unknown variable, $a, b$, and $c$ are constants. The solution to the quadratic equation is called quadratic formula and is given by:
$$
x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}
$$
Write the quadratic formula in $\mathrm{IAT}_{\mathrm{E}} \mathrm{X}$.
This semester, we will learn about functions. Use $\mathrm{L}_{\mathrm{E}} \mathrm{E} X$ to write the following function: $f: \mathbb{Z} \mapsto \mathbb{N}$ defined by
$$
f(x)= \begin{cases}2 x & \text { if } x \geq 0 \ -2 x-1 & \text { if } x<0\end{cases}
$$
We will learn about set theory in this course. Use LTEXto write the following sets:
$$
\begin{gathered}
V={x \in \mathbb{Z} \mid x<100} \cap{x \in \mathbb{Z} \mid \mathrm{x} \text { is prime }} \
V \subset W
\end{gathered}
$$
We will also learn about Boolean formulas and logic. Use LTEXto write the following Boolean formula:
$$
((\alpha \rightarrow \beta) \wedge(\beta \rightarrow \gamma)) \rightarrow(\alpha \rightarrow \gamma)
$$
Consider the following statements about integers:
For every $\mathrm{x}$, there is a $\mathrm{y}$, such that $x+y=0$
There is a $\mathrm{y}$, such that for every $\mathrm{x}$, we have $x+y=0$
In symbols, these statements are written respectively:
$\forall x \exists y x+y=0$
$\exists y \forall x x+y=0$
Use ATEXto write these two statements.
Use $\mathrm{HT}_{\mathrm{E}} \mathrm{X}$ to write the following proof verbatim (as is) including the square, mark of end of proof:
If $x$ is even, then $x^2$ is even.
Proof. $x$ is an even number.
$\exists a \in \mathbb{Z}$ such that $x=2 a$
$$
x^2=(2 a)^2=4 a^2=2\left(2 a^2\right)
$$
Let $c=2 a^2, c \in \mathbb{Z}$
$$
x^2=2 c
$$
Therefore, $x^2$ is even.
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