PURE MTH 2106 - Algebra II | Course Outlines

PURE MTH 2106 - Algebra II

North Terrace Campus - Semester 1 - 2018

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 in the physical sciences. 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. Homomorphism and isomorphism 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.

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Course Details

Course Code	PURE MTH 2106
Course	Algebra II
Coordinating Unit	Mathematical Sciences
Term	Semester 1
Level	Undergraduate
Location/s	North Terrace Campus
Units	3
Contact	Up to 3.5 hours per week
Available for Study Abroad and Exchange	Y
Prerequisites	MATHS 1012
Assessment	ongoing assessment 30%, exam 70%

Course Staff

Course Coordinator: Associate Professor Nicholas Buchdahl

Course Timetable

The full timetable of all activities for this course can be accessed from .

Course Learning Outcomes

Appreciate that common features of certain mathematical objects can be abstracted and studied.
Understand equivalence relations and partitions.
Understand the concepts of groups, group homomorphism and isomorphism and related notions.
Be familiar with common examples of groups of both finite and infinite order.
Be able to construct and work with related objects: subgroups, cartesian products, quotient groups.
Understand the concepts of vector space, linear transformation, isomorphism and related notions.
Be able to construct and work with related objects: subspaces, sums, quotient spaces, dual spaces.
Be able to represent a linear transformation by a matrix with respect to given ordered bases.
Understand the significance of Jordan canonical form.
Understand the notion of bilinear form and inner product.
Be familiar with various methods of proof, including direct proof, constructive proof, proof by contradiction, induction.
Develop skills in creative and critical thinking, problem solving, logical writing.

最新糖心Vlog Graduate Attributes

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

最新糖心Vlog Graduate Attribute	Course Learning Outcome(s)
Deep discipline knowledge informed and infused by cutting edge research, scaffolded throughout their program of studies acquired from personal interaction with research active educators, from year 1 accredited or validated against national or international standards (for relevant programs)	all
Critical thinking and problem solving steeped in research methods and rigor based on empirical evidence and the scientific approach to knowledge development demonstrated through appropriate and relevant assessment	all
Teamwork and communication skills developed from, with, and via the SGDE honed through assessment and practice throughout the program of studies encouraged and valued in all aspects of learning	11,12
Career and leadership readiness technology savvy professional and, where relevant, fully accredited forward thinking and well informed tested and validated by work based experiences	12
Self-awareness and emotional intelligence a capacity for self-reflection and a willingness to engage in self-appraisal open to objective and constructive feedback from supervisors and peers able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate	12

Learning Resources
Required Resources

None.

Recommended Resources
1. Fraleigh, J. B.: A first course in abstract algebra (Addison Wesley).
2. Durbin, J. R.: Modern algebra (Wiley).
3. Herstein, I. N.: Topics in Algebra (Wiley).
4. Lay, D. C.: Linear algebra and its applications (Pearson).
5. Lipschutz, S.: Linear algebra (Schaum's Outline Series).
6. Katznelson, Y. & Katznelson, Y. R.: A (terse) introduction to linear algebra (AMS).
Online Learning

This 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 Modes

This course relies on lectures as the primary delivery mechanism for the material. Tutorials supplement the lectures by providing exercises and example problems to enhance the understanding obtained through the lectures. Written assignments aid the learning of the material and provide assessment opportunities for students to gauge their progress and understanding.

Workload

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

Activity Quantity Workload Hours

Lectures 36 90

Tutorials 6 21

Assignments 5 45

Total 156

Learning Activities Summary
Lecture Outline
1. Equivalence relations (1 lecture).
2. Groups, subgroups, symmetries, cyclic groups (3 lectures).
3. Permutations, symmetric and alternating groups (2 lectures).
4. Isomorphism of groups (1 lecture).
5. Cosets and Lagrange's Theorem (3 lectures).
6. Group homomorphisms (2 lectures).
7. Normal subgroups and factor groups, simple groups, First Isomorphism Theorem (3 lectures).
8. Vector spaces, subspaces, linear independence, basis, dimension (3 lectures).
9. Linear and direct sums of spaces, quotient spaces (2 lectures).
10. Linear transformations (1 lecture).
11. Matrix with respect to basis, eigenvectors, similarity, dimension theorem (2 lectures).
12. Projections, invariant spaces (1 lecture).
13. Linear functionals and the dual space, second dual space (1 lecture).
14. Bilinear forms, congruent matrices, symmetric bilinear forms, quadratic forms (2 lectures).
15. Inner products, norm, distance, orthogonality (3 lectures).
16. Linear operators, adjoints (3 lectures).
17. Jordan canonical form (2 lectures).
Tutorial Outline
1. Tutorial 1: Groups.
2. Tutorial 2: Permutations, isomorphism.
3. Tutorial 3: Normal subgroups, quotient groups.
4. Tutorial 4: Sums of spaces.
5. Tutorial 5: Matrix of a linear transformation, linear functionals.
6. Tutorial 6: Inner products.
The lecture contents will be adjusted based on students' actual learning progress and outcome.
Specific Course Requirements

None.

The 最新糖心Vlog'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.

Assessment Summary

Component	Weighting	Objective Assessed
Assignments	15%	all
Tutorials	2.5%	all
Mid-term test	22.5%	1-5, 11, 12
Final Exam	60%	all

Assessment Related Requirements

An aggregate score of at least 50% is required to pass the course.

Assessment Detail

Assessment Item	Distributed	Due Date	Weighting
Assignment 1	week 2	week 3	3%
Assignment 2	week 4	week 5	3%
Assignment 3	week 6	week 7	3%
Assignment 4	week 8	week 9	3%
Assignment 5	week 10	week 11	3%
Mid-term test	week 6	week 6	22.5%

Attendance at tutorials will count 2.5% towards the final mark for the course.

Submission

Assignments will have a 2-week turn-around time for feedback to students.

Course Grading

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 .

Student Feedback

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SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the 最新糖心Vlog to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
Student Support
Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
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Authorised by:	Deputy Vice-Chancellor and Vice-President (Academic)
Maintained by:	Course Outlines Administrator

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