33290 Statistics and Mathematics for Science
Warning: The information on this page is indicative. The subject outline for a
particular semester, location and mode of offering is the authoritative source
of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.
Subject handbook information prior to 2015 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Requisite(s): 33190 Mathematical Modelling for Science OR 33130 Mathematical Modelling 1
These requisites may not apply to students in certain courses. See access conditions.
Anti-requisite(s): 33230 Mathematical Modelling 2 AND 35101 Introduction to Linear Dynamical Systems AND 35102 Introduction to Analysis and Multivariable Calculus AND 35151 Introduction to Statistics AND 37131 Introduction to Linear Dynamical Systems AND 37132 Introduction to Mathematical Analysis and Modelling AND 37151 Introduction to Data Analysis
Description
This subject covers studies of simultaneous linear equations and their occurrence in scientific problems; methods for solving these equations using matrices and determinants; eigenvalues and eigenvectors; vectors in two and three dimensions; products of vectors; spatial geometry and coordinate systems; functions of several variables; partial derivatives; optimisation and method of least squares; probability with a focus on the determination of the reliability of a system of components in various engineering contexts; variance, skewness and kurtosis; and probability distributions, conditional probability and bi-variate probability. The computer algebra system Mathematica is used throughout the subject as an aid to computation, graph plotting and visualisation.
Subject objectives
Upon successful completion of this subject students should be able to:
| 1. | understand the way in which probability can supply useful tools and resources to model real world problems |
|---|---|
| 2. | use the terminology and concepts of probability |
| 3. | use formal and informal language to demonstrate understanding of these concepts |
| 4. | demonstrate knowledge of all assumptions underlying probability techniques |
| 5. | demonstrate a high level of skill in checking whether the assumptions underlying probability techniques are satisfactory in particular situations |
| 6. | use the computer system Minitab to perform calculations and explore statistical ideas relevant to the subject content. |
| 7. | understand the way in which mathematics can provide useful tools and resources to real world problems |
| 8. | use mathematical terminology and concepts |
| 9. | use formal and informal language to demonstrate understanding of these concepts |
| 10. | demonstrate a satisfactory level of skill in the computational techniques covered in the subject content |
| 11. | use the computer system Mathematica to perform calculations and explore mathematical ideas relevant to the subject content |
| 12. | be aware of the historical context of mathematical development. |
| 13. | communicate the above knowledge clearly, logically and critically |
| 14. | apply the subject matter covered in lectures, tutorials, laboratories and assignments to previously unseen problems. |
This subject also contributes specifically to the development of following course intended learning outcomes:
- An understanding of the nature, practice and application of the chosen science discipline. (1.0)
Contribution to the development of graduate attributes
This subject contributes to the development of the graduate attributes of disciplinary knowledge and its appropriate application and an enquiry-oriented approach. This subject provides the disciplinary knowledge and skills for the analysis of data which can be gathered in experimental situations in a wide variety of sciences. These technical skills are evaluated through the problems in the tutorial and laboratory classes. It also emphasises the need to critically evaluate the nature of the data in order to ensure that appropriate statistical techniques are used and to report the results of the statistical analysis in appropriate ways. These aspects are examined in the assignments which present data sets for analysis but leave the students to determine the appropriate methods of analysis. These assignments can be completed by students in groups in order to develop communication skills and teamwork skills including time management and organisation skills.
Teaching and learning strategies
Spring Session:
Lectures: 3 hrs per week
Tutorials: 1hr per week
Computer laboratories: 1hr per week
Summer Session:
Lectures: Three 120 minute lectures per week in December and two 120 minute lectures per week in January
Tutorials: Three 60 minutes tutorials per week in December and two 60 minutes tutorials per week in January
Computer labs: Five drop-in sessions in the computer lab during the semester
Content
The major topics covered in this subject are: Descriptive statistics, discrete and continuous random variables, normal distribution, inference on population means, inference on population proportions, goodness of fit tests and simple linear regression. Linear modeling,matrices, eigenvalues and eigenvectors, functions of several variables, least squares and optimisation methods.
Assessment
Assessment task 1: Weekly Exercises
| Objective(s): | This assessment task contributes to the development of course intended learning outcome(s): 1.0 |
|---|---|
| Type: | Exercises |
| Weight: | 35% |
| Criteria: | Correct use of terminology; correct choice and use of problem solving strategies and procedures |
Assessment task 2: Examination
| Type: | Examination |
|---|---|
| Weight: | 65% |
| Criteria: | Correct use of terminology; correct choice and use of problem solving strategies and procedures; |
Minimum requirements
Student must obtain at least 40% of the marks available for the final examination in order to pass this subject. If 40% is not reached, an X grade fail may be awarded for the subject, irrespective of an overall mark greater than 50.
The final mark will be a combination of marks for all components of the assessment. Students must gain a combined mark of greater than 50% to pass the subject.
Students who receive between 40% and 50% for their final mark will be invited to sit for a supplementary examination. An overall mark 50P will be awarded to students who pass the supplementary examination. Students in this position will be contacted by email.
Recommended texts
Mathematics component textbook
J Stewart, Multivariable Calculus, Concepts and Contexts, 4th edition. Cengage Learning, 2009
Statistics component textbook
Robin H. Lock, Patti Frazer Lock, Kari Lock Morgan, Eric F. Lock, Dennis F. Lock.
Unlocking the Power of Data. Wiley, 2013.
You may want to buy a copy of the book yourself. If you do make sure that you are purchasing the book packaged with the WileyPLUS registration card so that you can access further resources at WileyPLUS. To do this either buy from the university bookshop who have ordered the correct stock as detailed below
Paperback
Statistics: Unlocking the Power of Data, 1st Edition Binder Ready Version + WileyPLUS Card
ISBN : 978-1-118-63197-3
Hardcover
Statistics: Unlocking the Power of Data, 1st Edition + WileyPLUS Card
ISBN : 978-1-118-56631-2
or purchase from WileyDirect.
http://www.wileydirect.com.au/buy/statistics-unlocking-power-data-1st-edition/
If you buy a copy of the book using the book ISBN only then you will not get a WileyPLUS access code and you will have to buy that separately (a more expensive option).
References
Devore, J.L. & Farnum, N.R. Applied Statistics for Engineers and Sciences, 2nd Ed. Cengage Learning, 2004.
Other resources
U:PASS
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 that subject, and who has a good WAM. The leader will typically prepare questions for you to work on, or if you have specific questions or things you’re not clear on, you can bring them along, and the leader will get the group to work on that. 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 in My Student Admin https://onestopadmin.uts.edu.au/. You’ll find it listed in the area where you sign up for lectures, tutorials, etc. Note that sign up is not open until week 1, as it’s voluntary and only students who want to go should sign up. Note that you don’t have to be struggling in the subject to attend U:PASS – frequently students who are already doing well will do even better after attending U:PASS. If you have any questions or concerns about U:PASS, please contact Georgina at upass@uts.edu.au, or check out the website: http://www.ssu.uts.edu.au/peerlearning/index.html
