Contact | Description | Topics | Texts | Notes | Lectures | Assessment and Assignments |
MAST30026 |
Semester II 2022 |
The exam assesses whether you can write quality solutions to questions in an exam setting. So the main goal of the class is to learn to write quality, well presented solutions, that communicate well and thoroughly to the reader. Whether or not you get a correct answer has much less importance than whether your exposition is of good quality.
To help learn this skill, we will provide three "proof writing" sessions
a week, in the same room as the lecture, in the hour before class.
These are not required,
you decide whether you want to take advantage of
this resource or not. It is during these sessions that we will provide models
for writing solutions to exam questions.
These sessions will be available live streamed and recorded, via
the usual Lecture capture.
https://canvas.lms.unimelb.edu.au/courses/129807
The goal is to be able to write quality solutions in an exam setting.
Lecturer: Arun Ram, 174 Peter Hall, email: aram@unimelb.edu.au
Time and Location: Zoom link on Canvas
https://canvas.lms.unimelb.edu.au/courses/129807
Lecture: Monday 9:00-10:00 Russell Love Theatre, Peter Hall Building,
Lecture: Wednesday 9:00-10:00 Russell Love Theatre, Peter Hall Building,
Lecture: Friday 10:00-11:00 Russell Love Theatre, Peter Hall Building,
The lectures will be live streamed by the usual Echo 360/Canvas delivery
If there are no technology glitches, each lecture will also be Zoom recorded
and made available on Echo360 (accessible through Canvas) within 7 days
after the live lecture.
You will do well on the exam if you are able to write solutions in the same
model as in the assignment solutions and the proof writing sessions
without the need for notes.
This is the skill that will be assessed on the exam.
The tutorials will begin on Friday of Week 1 (July 29).
In the first tutorial the "assignment marking exercise groups" will
be allocated. If you do not attend the first tutorial the tutor will assign
you to a group without your input.
Practice class: Monday 15:15-16:15 Online,
Tutor: Weiying Guo
Practice class: Wednesday 11:00-12:00 in Peter Hall 213,
Tutor: Arun Ram
Practice class: Friday 11:00-12:00 in Peter Hall 213,
Tutor: Arun Ram
A key part of Lecture time is the Ask me a question time. Given that we will hold the "Proof writing workshop" in the hour before lecture these will probably morph into the "Ask me a question" time for the 10 minute slot between class periods. The official lecture starts at 5 min past the hour.
Consultation hours: Arun Ram, Monday-Wednesday 10-11am,
Student Representatives: Haris Rao murao@student.unimelb.edu.au and Jiani Xie jianix1@student.unimelb.edu.au
Facebook group:
https://www.facebook.com/groups/????????/
The lecturer and tutors will not be reading, looking at, or participating
in the Facebook group. If you wish to have the lecturer or tutors
read or participate, hold the discussion on Ed Discussion
(which has math equation/LaTeX capability).
The Ed Discussion link for this course
is available through Canvas.
https://canvas.lms.unimelb.edu.au/courses/129807
Methods and mechanics for teaching, and how to improve teaching
and learning are topics that I think about quite alot. One piece of
writing that I have done on the subject is
Teaching Math in The Next Life
which might also be helpful to students taking this course. Certainly
we will discuss many of these topics in class. I would be very grateful
for any reactions/thoughts/discussion that you can give me on this
writing (and any of the other resources on this page).
The homework assignments are at the following links: (total 7% each = 5% for the first submission +2% for the second submission)
The first deadline is for you to submit your solutions to the assignment questions. Your submission will be marked by the tutors. The first submission of each assignment is worth 5% of the total mark for the course.
After the first submission you will receive 4 assignments to 'mark' (the submissions of the others in you 'assignment marking group'). Only by reading solutions and trying to do marking yourself, do you learn how to optimise your marks on the exam. Read the solutions, provide feedback, and assign a mark for each question. You may be asked to provide justification for the mark you assign (so keep records of the marking scheme you used for each question). Submit your "marking" of the 4 assignments as the second submission of the assignment. Tutors will allocate marks for your second submission based on how conscientiously you undertake this exercise. The second submission of each assignment is worth 2% of the total mark for the course.
Because the assignment solutions will be released immediately after the due date/time, no late submissions will be accepted. If you miss a submission and you have a valid reason (medical certificate or equivalent), then you will be given the option to recover the marks for that assignment by making 3 distinct handwritten copies of the assignment solutions and one handwritten copy of the sample exam solutions.
It is recommended that you do and submit the assignments in the same way that you will for the exam: handwritten, a new page for each question, very clear exposition so that the marker can follow your argument easily, scanned with Camscanner, and uploaded question by question into Gradescope. One purpose of the assignments is to prepare your exam taking skills.
Assessment will be based on three written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).
Almost everybody seems to agree that the "50 pages" doesn't make much sense in our modern technological world where some assignments might even be submitted in video form (the handbook entry has not been changed for more than 10 years) and a better estimate is to note that the handbook entry says that Total time commitment (should average) 170 hours. If we spread this over 14 weeks (12 class and 2 weeks exam study), we get 12.14 hours per week, and then if we subtract the number of class and tutorial hours per week (4) then we get 8.14 hours per week, and if we spread 12 weeks of 8 hours over 3 assignments then we get
4*8.14=32.6, as the average number of hours of study and work to complete each assignment.If you are spending more time than this, then please contact us immediately so that we can help you to make your study more efficient and effective so that you will be able to complete the necessary work for this class in this expected time commitment timeframe.
If you are spending less time than this, then maybe you should think twice about whether you will do well on the final exam.
The exam assesses whether you can write quality solutions to questions in an exam setting. So the main goal of the class is to learn to write quality, well presented solutions, that communicate well and thoroughly to the reader. Whether or not you get a correct answer has much less importance than whether your exposition is of good quality.
To help learn this skill, we will provide three "proof writing" sessions a week, in the same room as the lecture, in the hour before class. These are not required, you decide whether you want to take advantage of this resource or not. It is during these sessions that we will provide models for writing solutions to exam questions.
The following notes written by Arun Ram and provide a good pcture of how I think about and work with this subject.
References | Proof machine (How to do proofs) | Vocabulary |
Further references for useful comparison/contrast are:
If you don't communicate with us, then we can't help you. We'll do our best, but it is much easier if you take some responsibility too by asking questions and communicating in class and in tutorial.
As explained in the writing
Teaching Math in The Next Life,
almost certainly, I will build the exam
by choosing the questions randomly from my problem lists for the course.
These problem lists for this course are the following.
The handbook entry for this course is at https://handbook.unimelb.edu.au/2022/subjects/mast30026. The subject overview that one finds there:
This subject provides a basis for further studies in modern analysis, geometry, topology, differential equations and quantum mechanics.It introduces the idea of a metric space with a general distance function, and the resulting concepts of convergence, continuity, completeness, compactness and connectedness. The subject also introduces Hilbert spaces: infinite dimensional vector spaces (typically function spaces) equipped with an inner product that allows geometric ideas to be used to study these spaces and linear maps between them.
Topics include: metric and normed spaces, limits of sequences, open and closed sets, continuity, topological properties, compactness, connectedness; Cauchy sequences, completeness, contraction mapping theorem; Hilbert spaces, orthonormal systems, bounded linear operators and functionals, applications.