Mathematics and Biostatistics

Code:

MI071104

Acronym:

MATBIO

Keywords
Classification	Keyword
OFICIAL	Physical Sciences

Instance: 2012/2013 - 1S

Active?	Yes
Responsible unit:	Applied Chemistry Laboratory
Course/CS Responsible:	MSc in Pharmaceutical Sciences

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MICF	256	Official Curriculum	1	-	6	65	175,5

Teaching language

Portuguese

Objectives

It is aimed that at the end of the course the student has acquired:
1. basic techniques of integral calculus, essencial for the construction and qualitative analysis of statistic and or/ deterministic mathematical models (epidemiological models of transmission of infectious diseases, pharmacokinetic models, population dynamics models, ...)
2. enough knowledge on probability theory to the
understanding of statistical inference theory
3. several techniques of statistical inference; in particular
it is aimed that the student knows the mathematical model
that is behind each technique as well as the assumptions
of the model
4. knowledge on how to choose and apply the learned statistical techniques to problems related to the Health
and Biological Sciences
5. knowledge on how to interpret and criticize the results
obtained by application of the learned statistical tecnhiques
(either in their own works or in others´works)
6. familiarity with a software on statistical analysis.

Learning outcomes and competences

Those resulting from the compliance of the curricular unit objectives (explicited in the previous item) 

Working method

Presencial

Program

I. Reviews: logarithm and exponential functions; trignometric functions; derivatives and differentiation.

II. Integral Calculus

1. Riemann integral on one variable
a) Notion of Riemann integral as the area with sign of the region delimited by the graph of a function
b) Basic properties of integration
c) Fundamental theorem of calculus
d) integrals through primitives

2. Elementary notions on primitives
1. The notion of primitive
2. Algebraic rules for primitives
3. Primitives of polynomial functions
4. Primitives of trigonometric functions
5. Primitives by the substitution method
6. Primitives by parts

3. Improper integrals with unlimited limits of integration

III. Ordinary Differential Equations
1. First order ordinary differential equations
a) linear first order differential equations
b) separable differential equations

Application to pharmacokinetic models and population dynamics models.

IV. Probabilities
1. Introduction to the notion of probability distribution
a) the concept of probability
b) discrete and continuos random variables
c) probability density and probability distribution functions
d) quantiles, measures of central tendency (mean, median and mode), measures of dispersion (variance, standard deviation)

2. Discrete multivariate probability distributions:
a) joint probability function, marginal probabilities
b) independent random variables
c) mean, covariance and correlation.

3. Most common probabilistic models:
a) uniform (discrete and continuous), binomial, multinomial, Poisson, normal (gauss), log-normal, chi-squared, Student-t, Snedecor-F, exponential.
b) relations among some distributions
 
4. Samples of independent and identically distributed
random variables
a) sample distribution (empirical cumulative distribution function, histogram, boxplot)
b) sample associated statistics (sample proportion,
sample mean, sample variance, ...)
c) law of large numbers
d) central limit theorem.
e) sample mean as a random variable

V. Statistical Inference

1. Confidence intervals.
Confidence intervals for the mean, variance and proportion.

2. Hypothesis tests:
a) type I and type II errors; significance level
and power of a test
b) p-value of a test

c) hypothesis tests and confidence intervals

d) parametric tests for the mean and for the proportion

Mandatory literature

M. Spivak; Calculus, Publish or Perish; fourth edition , 2008. ISBN: ISBN-13: 978-0914098911
J. Stewart; Calculus : early transcendentals, Thonson Brooks/Cole, 2008. ISBN: 978-0-495-38273-7
A.C. Pedrosa, S.M.A. Gama; Introdução Computacional à Probabilidade e Estatística, Porto Editora, 2004. ISBN: 972-0-06056-5
W.W. Daniel; Biostatistics: a foundation for analysis in the health sciences, John Wiley and sons , 1999. ISBN: 0-471-16386-4

Teaching methods and learning activities

All the theory is given in the theoretical classes using slides prepared by the lecturer and using examples from the real life whenever possible. All the practical part of the course (exercise solving and software use) is given in the exercise classes under the supervision of the teacher.

 

 

Software

SPSS- Statistical Package for the Social Sciences

keywords

Physical sciences > Mathematics > Statistics
Physical sciences > Mathematics > Mathematical analysis

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	70,00
	Teste		35,00
	Exame		65,00
	Total:	-	100,00

Eligibility for exams

Terms of frequency: - Student attendance to the classes is mandatory. Those students whose attendance is lower than 2/3 of the classes effectively taught are considered as without attendance, as long as these classes represent more than 50% of the classes predicted.
- Student attendance to the classes is mandatory. Those students whose attendance is lower than 3/4 of the classes effectively taught are considered as without attendance, as long as these classes represent more than 50% of the classes predicted.
- Attendance to Theoretical classes is not compulsory.

Calculation formula of final grade

Formula Evaluation: The final mark consists of two parts:
Part I: not compulsory; evaluation test with the mark of 7/20, evaluating parts II and III from the syllabus of the curricular unit-

Part II:  final examination with the mark of 20 points (7 of which can be obtained from the evaluation test described above)

Examinations or Special Assignments

Not applicable.