33290 Statistics and Mathematics for Science
Warning: The information on this page is indicative. The subject outline for a
particular session, 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 2021 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 consists of two components: Statistics and Mathematics:
- The Statistics component focuses on data analysis. It aims to show students how to collect and analyse data, and how to draw valid conclusions from the data. It begins with a discussion of how to sample from a population, and how to describe the data collected. This is followed by a discussion of how to form and test hypotheses about the population using the data collected from the sample.
- The Mathematics component 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. The computer algebra system Mathematica is used as an aid to computation, graph plotting and visualisation.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | select and produce appropriate graphical, tabular and numerical summaries of variables in a data set, and summarise such information |
|---|---|
| 2. | distinguish between observational and experimental studies, and draw conclusions appropriate to each type of study |
| 3. | determine whether an interval or a test is more appropriate for addressing a particular question, and apply these concepts to answer questions using real data involving a single variable |
| 4. | choose the appropriate type of inference to answer questions using real data involving several variables |
| 5. | analyse, assess and critique statistical arguments of the type found in the popular press and in scholarly publications |
| 6. | summarise the way in which mathematics can provide useful tools and resources to real world problems |
| 7. | communicate the concepts of mathematics using proper terminology, as well as formal and informal language |
| 8. | demonstrate a satisfactory level of skill in the computational techniques covered in the subject content |
| 9. | Perform calculations using the computer system Mathematica to explore mathematical ideas relevant to the subject content |
| 10. | apply the knowledge and skills covered in lectures, tutorials, laboratories and assignments to previously unseen problems |
Contribution to the development of graduate attributes
This subject contributes to the development of the following graduate attributes:
1. Disciplinary knowledge and its appropriate application.
The lectures and tutorial classes communicate knowledge and skills and demonstrate how to apply both the knowledge and skills to a variety of problems. This graduate attribute is measured in the assessment tasks 1 to 5.
2. An Inquiry-oriented approach.
The lectures discuss various ways to address a particular question, and students will develop skills in determining the correct approach themselves in the classes. This graduate attribute is measured in the assessment tasks 1 to 5.
3. Professional skills and their appropriate application.
The ability to work effectively and responsibly in a group is emphasised in the group work component of the in-class assessment.
4. Ability and motivation for continued intellectual development.
The ability to independently collect and critically evaluate information is assessed in the critiquing task where students must find articles in the media that use statistical methods and assess the use of statistical methods in the article.
6. Communication skills.
Presentation of written solutions to problems using appropriate language is emphasised in the assessments.
7. Initiative and innovative ability.
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. The subject 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 allow students to select 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
The presentation of this subject will consist of two 90 minutes of lectures, a 1 hour tutorial and a 1 hour laboratory class each week. The face-to-face classes will incorporate a range of teaching and learning strategies including the presentation of worked examples, discussion of readings and individual student problem solving. It is expected that students will supplement this with individual study and problem solving, with materials provided on UTSOnline to assist students in preparing for classes.
Feedback on progress with the statistics section is provided throughout the semester. The fortnightly exercises (Assessment Task 1) provide immediate feedback on progress, with further feedback provided during the statistics assessment tasks, (Assessment Task 3). Students can track their progress in the mathematics section using the Mastery tests which allow students mutliple attempts to reach the threshold level of understanding. If the threshold is not reached at the first attempt, feedback is provided to allow students to concentrate on topics they are yet master.
Content (topics)
The major topics covered in this subject are:
- Data collection - methods and limitations, Data analysis, Statistical estimation and Critical about data-based claims
- Linear modelling and operations with matrices, eigenvalues and eigenvectors, functions of several variables and an introduction to their calculus, an introduction to unconstrained and constrained optimisation techniques.
Assessment
Assessment task 1: Mathematics – Mastery Tests
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge and its appropriate application. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 7, 8 and 9 This assessment task contributes to the development of course intended learning outcome(s): .0, .0 and .0 |
| Type: | Quiz/test |
| Weight: | 50% |
| Length: | 50 minutes |
| Criteria: |
|
Assessment task 2: Final Examination Summer
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge and its appropriate application. |
|---|---|
| Objective(s): | This assessment task contributes to the development of course intended learning outcome(s): .0 and .0 |
| Type: | Examination |
| Weight: | 50% |
| Length: | 2 hours plus 10 minutes reading time |
| Criteria: |
|
Minimum requirements
Students must obtain at least 80% of the available marks in at least one attempt of each of the four mastery tests to
pass the subject.
Students who have not obtained 80% of the available marks in each of the four mastery tests by 5:00pm of the last day
of the teaching period will not be permitted to sit the final exam.
Also, students must achieve a mark of at least 40% in the final examination in order to satisfy the minimum requirements of the
subject. If 40% is not reached, an X grade fail may be awarded for the subject, irrespective of an overall mark greater than 50
Recommended texts
Statistics component textbook
Jay L. Devore, Probability and Statistics for Engineering and the Sciences 9th Ed. Brooks/COLE Cengage Learning, 2015.
ISBN : 978-1-305-25180-9
You may want to buy a copy of this book for yourself. It will be a useful resource throughout your studies.
Mathematics component textbooks
- J. Stewart, Calculus - concepts and contexts, Metric International 4th Edition, Cengage,
- D. C. Lay, Linear Algebra and its Applications, 3rd edition, Pearson Education, 2006.
References
- Devore, J.L. & Farnum, N.R. Applied Statistics for Engineers and Sciences, 2nd Ed. Cengage Learning, 2004.
- Wlliam Navidi, Statistics for Engineers & Scientists, 4th Ed. McGraw Hill Education, 2015.
- Robin H. Lock, Patti Frazer Lock, Kari Lock Morgan, Eric F Lock, Dennis F. Lock, Unlocking the Power of Data. Wiley, 2013.
- C. H. Edwards and D. E. Penney, Calculus with Analytic Geometry, 3rd or 4th Editions, Prentice Hall.
- S. L. Salas and E. Hille, Calculus: one and several variables, 7th edition, John Wiley and Sons, 1995.
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