33290 Statistics and Mathematics for Science

Subject coordinator

Name: Edward Lidums

Phone: 95142235

Room: CB01.15.38

Email: Ed.Lidums@uts.edu.au
 

Handbook 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/outcomes

After successfully completing this subject,
• In the Statistics stream you 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

• In the Mathematics stream you should be able to:

1. understand the way in which mathematics can provide useful tools and resources to real world problems;
2. use mathematical terminology and concepts;
3. use formal and informal language to demonstrate understanding of these concepts;
4. demonstrate a satisfactory level of skill in the computational techniques covered in the subject content;
5. use the computer system Mathematica to perform calculations and explore mathematical ideas relevant to the subject content;
6. be aware of the historical context of mathematical development.

• In both streams you should be able to:

1. communicate the above knowledge clearly, logically and critically; and,
2. apply the subject matter covered in lectures, tutorials, laboratories and assignments to previously unseen problems.

Contribution to graduate profile

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 emphasizes 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 organization skills.

Teaching and learning strategies

The subject consists of lectures (3 hrs per week), tutorials (1hr per week) and computer laboratories (1hr per week).

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.
 

Minimum requirements

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 must gain at least 40% on the final examination. If you do not get 40% in the examination, you will be awarded your exam mark and your assignments will not count.

Students who hand in all assignments and do better on the final examination than the combined mark will be given their examination mark.

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 text(s)

Statistics stream textbook

1. Montgomery, D.C. et.al. ( 2007) Engineering Statistics (Fourth edition) , John Wiley and Sons

Mathematics stream reference books only

1. R J Harshbarger and J J Reynolds , Mathematical applications, 7th Edition, 2004
2. Stewart, James (2001) Calculus Concepts and Contexts (Second edition) Brooks/Cole.