33230 Mathematics 2
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particular session, location and mode of offering is the authoritative source
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Subject handbook information prior to 2025 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 33130 Mathematics 1 OR 33190 Mathematical Modelling for Science OR 37131 Introduction to Linear Dynamical Systems
Anti-requisite(s): 33290 Statistics and Mathematics for Science AND 35101 Introduction to Linear Dynamical Systems AND 35102 Introduction to Analysis and Multivariable Calculus AND 35151 Introduction to Statistics AND 37132 Introduction to Mathematical Analysis and Modelling AND Spks Between C10154 and C10158
Description
This subject consists of two parts: multivariate calculus and an introduction to statistics. The mathematical part develops the mathematical skills required for mathematical modelling of systems involving more than one independent variable. The statistics part is an introduction to descriptive statistics, statistical inference and simple linear regression. Topics include linear algebra, solutions to sets of equations resulting from particular problems, eigenvectors and eigenvalues, partial derivatives, optimisation, multiple integrals and their applications, and probability with a focus on the determination of the reliability of a system of components in various engineering contexts.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | model real world problems in engineering practice using mathematical and statistical tools and resources |
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| 2. | use formal mathematical and statistical terminology and also informal (lay) language to express the concepts presented in the subject |
| 3. | demonstrate a high level of skill in the mathematical and statistical techniques covered in the subject by both formulating and solving problems in engineering and science |
| 4. | demonstrate understanding of the theoretical results which justify the use of these techniques |
| 5. | communicate mathematical and statistical knowledge clearly, logically and critically |
| 6. | use appropriate mathematical and statistical software packages to perform calculations and explore ideas relevant to the subject content |
| 7. | apply the subject matter covered in lectures, computer labs, tutorials and assignments to previously unseen problems and proofs, especially in engineering and science. |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Technically Proficient: FEIT graduates apply abstraction, mathematics and discipline fundamentals, software, tools and techniques to evaluate, implement and operate systems. (D.1)
- Collaborative and Communicative: FEIT graduates work as an effective member or leader of diverse teams, communicating effectively and operating within cross-disciplinary and cross-cultural contexts in the workplace. (E.1)
Contribution to the development of graduate attributes
Engineers Australia Stage 1 Competencies
This subject contributes to the development of the following Engineers Australia Stage 1 Competencies:
- 1.2 Conceptual understanding of the mathematics, numerical analysis, statistics, and computer and information sciences which underpin the engineering discipline.
- 3.2. Effective oral and written communication in professional and lay domains.
Faculty of Science Graduate Attributes:
Graduate Attribute 1 - Disciplinary knowledge
An understanding of the nature, practice & application of the chosen science discipline,
Graduate Attribute 2 - Research, inquiry and critical thinking
An understanding of the scientific method of knowledge acquisition. Encompasses problem solving, critical thinking and analysis attributes, and the ability to discover new understandings.
Graduate Attribute 3 - Professional, ethical and social responsibility
The ability to acquire, develop, employ and integrate a range of technical, practical and professional skills, in appropriate and ethical ways within a professional context, autonomously and collaboratively and across a range of disciplinary and professional areas. Time management skills, personal organisation skills, teamwork skills, computing skills, laboratory skills, data handling, quantitative and graphical literacy skills.
Graduate Attribute 5 - Communication
An understanding of the different forms of communication - writing, reading, speaking, listening - including visual and graphical, within science and beyond and the ability to apply these appropriately and effectively for different audiences.
Teaching and learning strategies
Lectures: Two 90 minute lectures per week
Lecture materials including detailed notes are provided in Canvas for students to read before the class. Concepts and definitions are explored through the use of both pure and applied examples. Students have the opportunity to make notes and question concepts.
Tutorials: One one-hour tutorial per week
Students are required to attempt problems posted in Canvas before they come to the tutorial. These problems develop the concepts delivered in the previous lecture. In class students can ask questions about areas they don't understand with either their peers or their tutors.
Computer labs: Three one-hour computer labs and eight mastery test sessions (four tests with a second chance sitting)
Students work in the computer labs individually and in pairs. There is a problem sheet made available in Canvas which students use to prepare before they come to the lab. During the class students interact with the tutors and other students to complete the problems. The three labs make use of a program called minitab. This practice allows students the opportunity to get feedback in preparation for the Mastery Tests.
The Mastery Tests are interspersed between the computer labs. The material covered in the computer lab relates to the subsequent Mastery tests. After each test submission students get immediate feedback on correct or incorrect responses. The maths study centre is then available as a support mechanism for students to get feedback on incorrect responses and work through correct solutions. The subject coordinator will offer further feedback as a third step.
Webassign is the program used for practice tests. These can be accessed online by students at any time during the semester and students receive immediate feedback after each question is submitted. These questions cover all of the subject materials.
Forms of attendance in this subject online flexible. There will be subject announcements indicating opportunities to attend campus, alternatively all activities can be completed online.
Content (topics)
Topics include: linear algebra including eigenvalues and eigenvectors and applications; 3D geometry and functions of several variables; partial derivatives; optimisation; multiple integrals and their applications; probability with a focus on the determination of the reliability of a system of components in various engineering contexts; descriptive statistics, probability distributions, statistical inference, introduction to linear regression.
Minitab is used in the statistics part of the subject. Other software will be used as appropriate.
Assessment
Assessment task 1: Mastery Test 1
| Intent: | To reaffirm required knowledge for success in 33230, and to become acquainted with the mastery process. This assessment task contributes to the development of the following science graduate attributes: 1. disciplinary knowledge Mastery Tests targets Problem posing and solving – ability to identify, assess and formulate problems relevant to one’s academic discipline and apply appropriate approaches and methods of problem solving. |
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| Objective(s): | This assessment task addresses subject learning objective(s): 2 This assessment task contributes to the development of course intended learning outcome(s): D.1 |
| Groupwork: | Individual |
| Weight: | 5% |
| Length: | 50 min |
| Criteria: | Correct interpretation of terminology, Correct choice of problem solving strategies and procedures. Correct choice of reasoning. |
Assessment task 2: Mastery Test 2
| Intent: | To provide feedback on basic skills and concepts in the material covered in weeks 1-3 of the statistics strand and weeks 1-2 of the mathematics strand. This assessment task contributes to the development of the following science graduate attributes: 1. disciplinary knowledge |
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| Objective(s): | This assessment task addresses subject learning objective(s): 2, 3, 6 and 7 This assessment task contributes to the development of course intended learning outcome(s): D.1 |
| Groupwork: | Individual |
| Weight: | 15% |
| Length: | 50 min |
| Criteria: | Correct use of terminology |
Assessment task 3: Mastery Test 3
| Intent: | To provide feedback on basic skills and concepts in the material covered in weeks 4-6 of the statistics strand and weeks 3-6 of the mathematics strand. This assessment task contributes to the development of the following science graduate attributes: 1. disciplinary knowledge |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 2, 3, 6 and 7 This assessment task contributes to the development of course intended learning outcome(s): D.1 |
| Groupwork: | Individual |
| Weight: | 15% |
| Length: | 50 min |
| Criteria: | Correct interpretation of terminology, Correct choice of problem solving strategies and procedures. Correct choice of reasoning. |
Assessment task 4: Mastery Test 4
| Intent: | To provide feedback on basic skills and concepts in the material covered in weeks 7-9 of the statistics strand and weeks 7-10 of the mathematics strand. This assessment task contributes to the development of the following science graduate attributes: 1. disciplinary knowledge |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 2, 3, 6 and 7 This assessment task contributes to the development of course intended learning outcome(s): D.1 |
| Groupwork: | Individual |
| Weight: | 15% |
| Length: | 50 min |
| Criteria: | Correct interpretation of terminology, Correct choice of problem solving strategies and procedures. Correct choice of reasoning. |
Assessment task 5: Final Exam
| Intent: | To comprehensively assess more advanced material across the subject, including material taken from all of the lectures in both the statistics and mathematics strands. This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary Knowledge 2. Research, inquiry and critical thinking 3. Professional, ethical and social responsibility 5. Communication |
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| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3, 4, 5 and 7 This assessment task contributes to the development of course intended learning outcome(s): D.1 and E.1 |
| Groupwork: | Individual |
| Weight: | 50% |
| Length: | 2 hours plus 10 minutes reading time |
| Criteria: | Correct use of terminology Correct choice and use of problem solving strategies and procedures Accurate Mathematical Reasoning Clarity of communication |
Minimum requirements
Students must achieve 50% in the final examination in order to pass the subject. A student who receives less than 50% for the examination, yet manages to achieve 50% or greater overall, will be awarded an X grade.
Recommended texts
Devore, Jay (2014) Probability and Statistics for Engineering and the Sciences Ninth Edition Cengage.
Stewart: "Calculus, Concepts and Contexts", 4e (2010), Cengage.
References
Mathematics:
McLelland, G. J. (1999) An Introduction to Matrices, Determinants and Linear Equations.
Department of Mathematical Sciences, UTS. (available on UTS Online)
Statistics:
Montgomery, D. C., Runger, G. C. & Hubele, N. F. (2011) Engineering Statistics, 5th edition, Wiley.
Other resources
Students are encouraged to make use of the collection of online videos made available on Canvas, as well as practise quizzes and weekly homework exercises on Webassign.
U:PASS
(UTS Peer Assisted Study Success) is a voluntary “study session” where you will be studying the subject with other students in a group. It is led by a student who has previously achieved a distinction or high distinction in the subject area, and who has a good WAM. Leaders will prepare activities for you to work on in groups based on the content you are learning in lectures and tutorials. It’s really relaxed, friendly, and informal. Because the leader is a student just like you, they understand what it’s like to study the subject and how to do well, and they can pass those tips along to you. Students also say it’s a great way to meet new people and a “guaranteed study hour”.
You can sign up for U:PASS sessions via U:PASS website http://tinyurl.com/upass2017 Note that sign up is not open until week 2, as it’s voluntary and only students who want to go should sign up. If you have any questions or concerns about U:PASS, please contact Georgina at upass@uts.edu.au, or check out the website.