1999 Pharmacy Handbook

Mathematics

Introduction
General objectives
Syllabus
Textbooks
Assessment

Introduction

Dr William Thiel
44 lectures, 18 tutorials and 25 hours of assignment work.
The subject aims to provide students with the necessary calculus and statistical techniques for the subjects of the pharmacy degree and prepare future graduates for the increasing use of computers in the profession.

General objectives

In this teaching program students are expected to develop:

understanding of the principal components of hardware and software involved in operating a computer; the use of stand-alone and networked PCs; the basic methods of differentiation and integration and their application to maxima and minima problems, rate equations and chemical kinetics; logarithmic scale and triangular graph papers; solution of simple ordinary differential equations; the principles of partial differentiation with an emphasis on application to thermodynamics and diffusion theory; the presentation of statistical data; probability distributions, the concept of a sampling distribution and application to the derivation of confidence intervals; making statistically based decisions using hypotheses testing; the theory of regression and correlation;
abilities in the areas of computer use; problem solving; logical, orderly thought and accuracy in working; program development and testing; application of mathematical models using calculus in the areas of physical chemistry, physical pharmacy and biopharmaceutics; selecting the appropriate statistical method to calculate a confidence interval or test a hypothesis;
an appreciation of the use of computers to store, manipulate and retrieve information; the application of calculus to physical and biological processes; the interpretation of simple clinical results using a range of statistical tests.

Syllabus

Computer studies

General introduction. Purpose and basic components of a computer. Hardware, software and operating systems.
Networking. The Monash student environment. Registration, login, security and password protection. Remote access. Networked printing. Quotas and limits.
The Internet. Browsing, searching and information retrieval using the WWW and the Internet.
Personal computers. IBM and standards in the computing industry. PC operating systems. Booting up and re-booting. Disks - capacity and industry standards, formatting options. Types of printer. Connecting, configuring and using a printer. Considerations involved in computer and printer purchase.
File maintenance. Creating and maintaining directories, subdirectories and files. Backup strategies and virus prevention.
Monash standard software. Using Word to create, edit, illustrate and format documents. Using Excel to solve problems, process data and present results in tabular or graphical form. Writing, recording and running macros.
Tutorial classes will be run in conjunction with the coursework and will provide opportunities to practise, understand and use the information presented. Computer access will be available during the whole of the undergraduate course.

Calculus

Differentiation. Limits, definition, product, quotient, function of a function, implicit differentiation, stationary points, turning points, points of inflection and function sketching.
Logarithmic plots. Exponential and logarithmic functions, semi-logarithmic and logarithmic plots.
Integration methods. By parts, algebraic substitution and partial fractions.
First-order rate processes. Definition, different physical processes obeying the law (eg radioactive decay, chemical reaction, microbiological growth, elementary pharmacokinetics), half-life and semi-logarithmic plots.
Zero, second and third-order reaction. The rate equations, their solutions and half-life.
Triangular charts. Graphical representation of three component systems.
Partial differentiation. Functions of several variables, first and second partial derivatives, geometric interpretation.
Integration. Definite integrals, area under a curve, infinite limits, approximate integration methods (trapezoidal rule).
Differential equations. Solution of ordinary differential equations by separation of variables and integrating factor methods. Partial differential equations, the unsteady state diffusion equations. Fick's Law of Diffusion.

Statistics

Presentation of sample data. Frequency tables, histograms and cumulative frequency distributions.
Measures of central tendency and dispersion. Mode, median, arithmetic and geometric mean. Skew of a distribution. Standard deviation, variance and degrees of freedom.
Probability distributions. General properties, the binomial, Poisson and normal distribution. Normal probability graph paper. The log normal distribution and log probability graph paper. Normal approximation to the binomial distribution, distribution of proportions.
Sampling. Random sampling, the Central Limit Theorem, calculation of sample size to attain a required accuracy.
Estimation. Point and interval estimates, Student's t-distribution. Confidence intervals for the mean and for the difference of two means (independent populations). The pairing of samples, confidence intervals for paired data. Confidence intervals for the difference of two proportions (independent populations). Confidence intervals for the variance, the chi-square distribution.
Hypothesis testing. Testing using confidence intervals. The H₀ and H₁ hypothesis, type 1 and 2 errors, one-sided and two-sided testing, p values, operating, characteristic curves.
Fitting a line. Least squares fit using partial differential calculus to develop the normal equations.
Regression theory. The mathematical model, residual variance, confidence intervals for slope, intercept and predicted Y value.
Correlation. Linear correlation coefficient.
Contingency tables. Test for independence testing several proportions, the chi-square distribution.

Textbooks

Recommended texts

Abbott P Calculus (Teach Yourself Books) 3rd edn, Hodder and Stoughton, 1992
Freund J E and Simon G A Modern elementary statistics 9th edn, Prentice-Hall, 1996

Reference books

Lentner M Introduction to applied statistics Prindle, Weber and Schmidt, 1975
Martin A N and others Physical pharmacy 4th edn, Lea and Febiger, 1993
White R How computers work 2nd edn, Ziff-Davis, 1995
Wonnacott T M and Wonnacott R J Introductory statistics 5th edn, Wiley, 1990

Assessment

Subject assessment will reflect the learning objectives outlined above. Methods of assessment will include:

Progress examination (May) (1.5 hours): 10%
End-of-year examination (2 hours): 90%