CS计算机代考程序代写 discrete mathematics PowerPoint Presentation

PowerPoint Presentation

MATH1061/MATH7861 Discrete Mathematics Semester 2, 2021 Lecture 1

Welcome to MATH1061 and MATH7861 – Discrete Mathematics

Lecturing staff: Sara Herke (course coordinator and lecturer – 1st half)
Office: 69-704
Phone: 34432411
Consultation hours:

Lecture Assistants:

Barbara Maenhaut (course coordinator and lecturer – 2nd half)
Office: 67-548
Phone: 33653258
Consultation hours:

Sara Herke

Lecture 1

How the course will work

Before each class:
• Watch one or two short videos and answer the related multiple-choice questions in edx (Edge).
• Read the related pages in the textbook, Discrete Mathematics with Applications by Susanna Epp,

4th or 5th (metric) edition, available in hard copy or e-book.
• Attempt the problems we will be working through in class.

In class:
• We will work through problems together to develop a deeper understanding of core concepts.
• You can ask questions to clarify anything you didn’t understand from the video/reading.
• We will discuss the importance of, and links between, concepts in the course.

After class:
• Revise material from videos, readings or classes as necessary.
• Apply what you have learned to solve problems (tutorial problems and/or assignment problems).
• Discuss any questions you have with peers, tutors, lecturers as necessary.

Expected workload for a #2 course at UQ is 10 hours per week.

3 hours per week (Mon 12pm, Wed 5pm, Fri 2pm)

3 hours per week (1 hour for each class)

1 hour per week tutorial, approximately 3 hours per week individual study

Blackboard demonstration – where to find edX, pre-class work, online discussion board (https://learn.uq.edu.au)

Sara Herke

Lecture 1

Assessment: MATH1061

Assignments (4) : 20%

Mid-semester Examination: 25% or 0%

Final Examination: 55% or 80%

Hurdles!!!

Grade 3: At least 40% of the marks on the final examination.

Grade 4: At least 45% of the marks on the final examination.

Grade 7: At least 80% of the marks on the final examination.

Assessment: MATH7861

Assignments (4) : 30%

Mid-semester Examination: 20% or 0%

Final Examination: 50% or 70%

MATH1061 and MATH7861 assignments and exams are different – make sure you complete the correct ones!

Ensure that you have read the ECP for the version of the course you are enrolled in!

Sara Herke

Lecture 1

Assignments:
Assignments will be available in pdf format on the course Blackboard page, approximately two weeks
before they are due. Each course has four assignments, due on the Thursdays of weeks 4, 7, 10 and 13.

MATH1061 and MATH7861 assignments are different – make sure you complete the correct ones!

Examinations:

The mid-semester examination will be on a Saturday, either 28 August, 4 September or 11 September, to be
scheduled by UQ. More details (cut-off for material on the exam) will be provided closer to the time.

The final examination will be scheduled by UQ and will be held in November in the examination period. The
final examination is cumulative.

Internal students will have their mid-semester and final examinations in person, invigilated on-campus.
External students will have their mid-semester and final examinations at the same time, but invigilated on
Zoom.

Sara Herke

Lecture 1

Course support: Lecturers and lecture assistants.
Tutorial staff.
First Year Mathematics Learning Centre – Room 443 in building 67

each weekday afternoon 2-4pm, tutors are available to help with any
first year mathematics course including MATH7861, also available via Zoom.

Online Discussion Board – a Q&A forum monitored by lecturers and tutors.
Maths@UQ – brush up on basic skills at your own pace

Support available (both MATH1061 and MATH7861):

Other support: Student Services, Library workshops, Faculty support

For details, see the Course Help tab on the Blackboard page

Sara Herke

Lecture 1

Course outline
Logic:

Symbolic logic is the basis for many areas of computer science.
It helps us to formulate mathematical ideas and proofs effectively and correctly!

Modern mathematics uses the language of set theory and the notation of logic.

Number theory and methods of proof:
You will learn how to structure a mathematical proof and how to apply various proof techniques. Along the
way we will prove many straightforward results about numbers, as well as some important theorems.

Set Theory:

Functions and relations:

Group theory:

Counting:

Graph theory:

You will learn about functions in a more general context than you see in your calculus classes. Functions are
a special type of relation, and relations are widely used throughout mathematics.

A group is a set along with a binary operation on that set; for example the set of integers and
addition of integers. Groups are fundamental objects in mathematics and have many interesting properties.

You will learn techniques for counting (which is a lot more complicated than it sounds).

A graph is a set of points and lines joining pairs of points. Graphs are widely used in modelling and are
also studied in their own right.

Some overlap with Year 11 and
12 Specialist Mathematics

Sara Herke

Lecture 1

The five sides and five diagonals of a regular pentagon are drawn on a piece of paper.
Two people play a game, in which they take turns to colour one of these ten line segments.
The first player colours line segments blue, while the second player colours line segments red.
A player cannot colour a line segment that has already been coloured.
A player wins if they are the first to create a triangle in their own colour, whose three vertices are also vertices
of the regular pentagon. The game is declared a draw if all ten line segments have been coloured without
a player winning. Determine whether the first player, the second player, or neither player can force a win.

The following question was on the Simon Marais
Mathematics Competition for undergraduate students in 2017.

Sara Herke

Lecture 1

Some more problems to get us started

2. Four non-zero real numbers 𝑎, 𝑏, 𝑐, 𝑑 are given, where 𝑏 + 𝑑 ≠ 0. If
𝑎

𝑏
+

𝑐

𝑑
=

𝑎+𝑐

𝑏+𝑑
show that 𝑎𝑐 < 0. 1. Let 𝑝, 𝑞 and 𝑟 be consecutive positive integers with 𝑝 < 𝑞 < 𝑟, and let 𝑎 = 𝑝 + 𝑟, 𝑏 = 𝑝𝑟 and 𝑐 = 𝑟 − 𝑝. Determine which of 𝑎, 𝑏, 𝑐 must be even. 5. The Königsberg Bridge Problem: Does there exist a route through the city that crosses each bridge exactly once and takes you back to the starting place? (No turning around on bridges.) 4. The Tower of Hanoi: Given a tower of 8 discs in decreasing size on one of three pegs, transfer the entire tower to one of the other pegs according to the following rules: (a) Move only one disc at a time. (b) Never move a larger disc onto a smaller disc. Is there a solution? If there is, what is the fewest number of moves needed to complete the transfer? 3. True or False: In every group of five people, there are two people who have the same number of friends within the group. Sara Herke Sara Herke Lecture 1 Solutions 1. Let 𝑝, 𝑞 and 𝑟 be consecutive positive integers with 𝑝 < 𝑞 < 𝑟, and let 𝑎 = 𝑝 + 𝑟, 𝑏 = 𝑝𝑟 and 𝑐 = 𝑟 − 𝑝. Determine which of 𝑎, 𝑏, 𝑐 must be even. Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Lecture 1 Solutions 2. Four non-zero real numbers 𝑎, 𝑏, 𝑐, 𝑑 are given, where 𝑏 + 𝑑 ≠ 0. If 𝑎 𝑏 + 𝑐 𝑑 = 𝑎+𝑐 𝑏+𝑑 show that 𝑎𝑐 < 0. Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke Sara Herke

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