MY-ASSIGNMENTEXPERT™可以为您提供sydney MATH1004 Discrete Mathematics离散数学课程的代写代考和辅导服务！
这是悉尼大学 离散数学课程的代写成功案例。
MATH1004课程简介
This unit provides an introduction to fundamental aspects of discrete mathematics, which deals with ‘things that come in chunks that can be counted’. It focuses on the enumeration of a set of numbers, viz. Catalan numbers. Topics include sets and functions, counting principles, discrete probability, Boolean expressions, mathematical induction, linear recurrence relations, graphs and trees.
Prerequisites
At the completion of this unit, you should be able to:
- LO1. identify combinatorial objects involved in counting problems
- LO2. understand how to construct switching circuits representing Boolean functions
- LO3. factor numbers using sieve methods and use the Euclidean algorithm to compute greatest common divisors
- LO4. solve linear recurrence relations by using generating functions or characteristic equations.
MATH1004 Discrete Mathematics HELP（EXAM HELP， ONLINE TUTOR）
In the group $S_6$, how many cycles are of the form (12)(34)(56)? In the group $S_7$, how many cycles are of the form $(12)(34)(56)(7)$ ?
One labeling of the regular hexagon is the figure below, where any symmetry operation on the hexagon permutes the sets of elements that share a number. For example, the three edges numbered 4 may be interchanged with the three edges numbered 5 .
(a) Write the five permutations from $S_5$ that represent non-trivial rotations about an axis perpendicular to the plane of the hexagon.
(b) Write the three permutations from $S_5$ that represent reflections about axes between two opposite vertices (or, if you prefer, $180^{\circ}$ rotations about theses axes).
(c) Express the last three non-trivial symmetries of the regular hexagon as permutations from $S_5$, and describe what each does geometrically.
Consider the following six functions:
$$
\begin{aligned}
f_1(x) & =x & f_2(x) & =1-x \
f_3(x) & =\frac{1}{x} & f_4(x) & =\frac{1}{1-x} \
f_5(x) & =\frac{x}{x-1} & f_6(x) & =\frac{x-1}{x}
\end{aligned}
$$
Now think of these as a group under the operation composition. For example,
$$
\begin{aligned}
\left(f_2 \circ f_3\right)(x) & =f_2\left(f_3(x)\right) \
& =f_2\left(\frac{1}{x}\right) \
& =1-\frac{1}{x} \
& =\frac{x-1}{x} \
& =f_6(x) .
\end{aligned}
$$
Show that if $G$ is a group and $x, y \in G$, then $(x y)^{-1}=y^{-1} x^{-1}$..
In $\mathbb{Z}_{13}$
(a) what is the additive inverse of [5]?
(b) for what $m$ and $n$ does $13 m+5 n=1$ ?
(c) what is the multiplicative inverse of [5]?
(d) what is the square root of $[-1]$ ?
MY-ASSIGNMENTEXPERT™可以为您提供sydney MATH1004 Discrete Mathematics离散数学课程的代写代考和辅导服务！
