PURE MTH 7106 - Algebra
North Terrace Campus - Semester 1 - 2023
General Course Information
Course Code PURE MTH 7106 Course Algebra Coordinating Unit School of Mathematical Sciences Term Semester 1 Level Postgraduate Coursework Location/s North Terrace Campus Units 3 Contact Up to 3 hours per week Available for Study Abroad and Exchange Y Assumed Knowledge MATHS 1012 Course Description Knowledge of group theory and of linear algebra is important for an understanding of many areas of pure and applied mathematics, including advanced algebra and analysis, number theory, coding theory, cryptography and differential equations. There are also important applications to physics and chemistry.
Topics covered are (1) Equivalence relations (2) Groups: subgroups, cyclic groups, cosets, Lagrange's theorem, normal subgroups and factor groups. Examples of finite and infinite groups, including groups of symmetries and permutations, groups of numbers and matrices. Homomorphisms and isomorphisms of groups. (3) Linear algebra: vector spaces, bases, linear transformations and matrices, subspaces, sums and quotients of spaces, dual spaces, bilinear forms and inner product spaces, and canonical forms.
Course Coordinator: Dr Raymond Vozzo
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning Outcomes1. Appreciate that common features of certain mathematical objects can be abstracted and studied.
2. Understand equivalence relations and partitions.
3. Understand the concepts of groups, group homomorphism and isomorphism and related notions.
4. Be familiar with common examples of groups of both finite and infinite order.
5. Be able to construct and work with related objects: subgroups, cartesian products, quotient groups.
6. Understand the concepts of vector space, linear transformation, isomorphism and related notions.
7. Be able to construct and work with related objects: subspaces, sums, quotient spaces, dual spaces.
8. Understand the notion of bilinear form.
9. Understand the significance of Jordan canonical form.
10. Be familiar with various methods of proof, including direct proof, constructive proof, proof by contradiction, induction.
11. Develop skills in creative and critical thinking, problem solving, logical writing and clear communication of mathematical ideas.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s)
Attribute 1: Deep discipline knowledge and intellectual breadth
Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.
Attribute 2: Creative and critical thinking, and problem solving
Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.
Attribute 3: Teamwork and communication skills
Graduates convey ideas and information effectively to a range of audiences for a variety of purposes and contribute in a positive and collaborative manner to achieving common goals.
Attribute 4: Professionalism and leadership readiness
Graduates engage in professional behaviour and have the potential to be entrepreneurial and take leadership roles in their chosen occupations or careers and communities.
- Fraleigh, J. B.: A first course in abstract algebra (Addison Wesley).
- Durbin, J. R.: Modern algebra (Wiley).
- Herstein, I. N.: Topics in Algebra (Wiley).
- Lay, D. C.: Linear algebra and its applications (Pearson).
- Lipschutz, S.: Linear algebra (Schaum's Outline Series).
- Katznelson, Y. & Katznelson, Y. R.: A (terse) introduction to linear algebra (AMS).
- Axler, S.: Linear Algebra Done Right (Springer).
Online LearningThis course uses Canvas for providing electronic resources, such as lecture notes, assignment papers, sample solutions, etc. It is recommended that students make appropriate use of these resourses.
Learning & Teaching Activities
Learning & Teaching ModesThis course runs in a "flipped classroom" model, whereby students are expected to watch the lecture topic videos and complete any necessary reading before coming to active learning classes (tutorials), which provide exercises and example problems to enhance the understanding obtained through the videos. Written assignments aid the learning of the material and provide assessment opportunities for students to gauge their progress and understanding.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload Hours Lecture videos 12 weeks 90 Tutorials 12 24 Assignments 5 40 Total 154
Learning Activities SummaryTopic Outline
(2) Groups: subgroups, cyclic groups, cosets, Lagrange's theorem, normal subgroups and factor groups. Examples of finite and infinite groups, including groups of symmetries and permutations, groups of numbers and matrices. Homomorphisms and isomorphisms of groups.
(3) Linear algebra: vector spaces, bases, linear transformations and matrices, subspaces, sums and quotients of spaces, dual spaces, bilinear forms and inner product spaces, and canonical forms.
Specific Course RequirementsNone.
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Component Weighting Objective Assessed Assignments 20% all Quizzes 15% all Mid-term test 15% 1-5, 10,11 Final Exam 50% all
Assessment Related RequirementsAn aggregate score of at least 50% is required to pass the course.
No information currently available.
SubmissionAssignments will have a 2-week turn-around time for feedback to students.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending
Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
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