Quantitative Methods

Code:

MV116

Acronym:

MQ

Keywords
Classification	Keyword
OFICIAL	Basic Sciences

Instance: 2010/2011 - 1S

Active?	Yes
Responsible unit:	Population Studies
Course/CS Responsible:	Integrated Masters Degree in Veterinary Medicine

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIMV	105	Plan 2007 to 2017	1	-	6	90	162

Teaching language

Portuguese

Objectives

The aim of this course is to familiarise first year students with basic mathematical/statistical concepts and techniques essential for formulating and understanding models in biology.

Program

I - Differential/Integral Calculus:
- A review of functions: algebraic, logarithmic, exponential. Limits and continuity. Differentiation: rules of differentiation, implicit differentiation. Applications of differentiation. Curve sketching.
- Functions of several variables: Introduction. Partial derivatives: definition and the geometric interpretation. Optimising functions of several variables.
- Introduction to Integral Calculus: Integration - the definitive integral and areas under a curve: The definitive integral. Standard integrals and methods of integration: by partial fractions. Impropers integrals. Applications in Biology.
- Differential Equations: Introduction. First order differential equations: variables separable differential equations. Applications: Deterministic model: exponential growth and decline in continuous time; Logistic and Gompertz model for limited population growth.
II - Descriptive statistics
Biological data and its graphical display; Descriptive statistics; Probability and probability distributions.
III - Statistical Inference
- Basic concepts of statistical inference: Sampling and sampling distributions; The Central Limit Theorem; Estimation and hypothesis testing; Confidence Intervals.
- Inferences concerning means: Hypothesis testing and Confidence Intervals - Inference for a mean of a population; Comparing two means (paired and independent samples); The F test for comparing two standard deviations .
- Inferences concerning proportions: Hypothesis testing and Confidence Intervals - Inference for a population proportion; Comparing two proportions (paired and independent samples); Comparing more than two proportions. Measuring associations with odds ratios and relative risk. Case-control and Cohort studies.
- Correlation and Linear regression: The regression model. The method of least squares. Hypothesis testing and Confidence Interval for the regression slope. Correlation coeficient. Residual analysis. Stochastic models and curve fitting: linear relationships, power and exponential laws.
IV - Computer sections: use of packages for mathematical and statistical analysis.

Mandatory literature

Eason G.; Mathematics and statistics for the bio-sciences. ISBN: 13-560541-5
Altman DG; Pratical Statistics for Medical Research, Chapman and Hall, 1991
Brown D.; Models in biology. ISBN: 0-471-93322-8
Dawson-Saunders Beth; Basic and clinical biostatistics. ISBN: 0-8385-0541-4
Busenberg S. ed.; Differential equations models in biology, epidemiology and ecology. ISBN: 3-540-54283-3

Complementary Bibliography

Fleiss Joseph L.; Statistical methods for rates and proportions. ISBN: 0-471-26370-2

Teaching methods and learning activities

The topics covered are introduced in the theoretical lectures, through an example of application in the biological sciences. In practical lessons students use SPSS software to solve complex exercises. Emphasis is given to teaching the need of understanding and using methods of formulating models, rather than the mechanical use of the techniques.

Software

PASW 18.00

Evaluation Type

Evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	90,00
	Total:	-	0,00

Calculation formula of final grade

The evaluation will have two components:
Writing: In the practical lessons or by final examination.
Practical: In the last week of lessons (1st time students) or by final examination (for the remaining students).

0.40xP + 0.60xW

W - Writing
P - Practical

The student must have at least 7 (out of 20) in each part.