Mathematics and Biostatistics

Code:

MI071104

Acronym:

MATBIO

Keywords
Classification	Keyword
OFICIAL	Physical Sciences

Instance: 2017/2018 - 1S

Active?	Yes
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	229	Official Curriculum	1	-	6	65	175,5

Teaching language

Portuguese

Objectives

The main goal of this course is that each student acquires basic skills on:

a) basic techniques of integral calculus, essential for analysing quantitatively mathematical models of statistical or deterministic type

b) minimum knowledge of probability theory in order to be able to understand statistical inference techniques

c) some knowledge about techniques of statistical inference; the main concern is that the student understands the mechanisms subsequent to the various techniques

d) how to adapt and apply the learnt statistical methodologies to concrete problems in the area of Natural and Health Sciences.

d) critical thinking and the ability to interpret the results obtained by applying statistical techniques (either in work done by the student or in another's work)

Learning outcomes and competences

At the end of the curricular unit, the student should be able to:

a) understand the notion of integrability and be able to perform integration calculus through the application  of the most common rules

b) understand the description of the most common probabilistic models

c) choose and apply the most adequate stastistical method to a given problem within the area of Natural and Health Sciences.

d) think critically and to interpret the results obtained by applying statistical techniques (either in work done by the student or by others).

Working method

Presencial

Program

I. Trigonometry

Derivatives, inverse trignometric functions and respective derivatives.

II. Cálculo integral
1. Riemann integral
a) Definition
b) Basic integration properties
c) Fundamental theorem of calculus
d) Computation of integral using primitives

2. Primitives
a) Definition
b) Algebraic rules
c) Primitives of polynomial functions
d) Primitives of trignometric functions
e) The substitution technique
f) Primitives by parts

3. Areas and volumes

4. Improper integrals

III. Probability
1. Preliminaries
a) notion of probability
b) discrete and continuous random variables
c) probability density function and distribution function 
d) quantiles, mean, median variance and standard deviation

2. Joint discrete probability distributions:
a) joint distributions, marginal distributions
b) independent random variables
c) mean and variance

3. Usual Probabilistic Models:
a) uniform, binomial, multinomial, Poisson, normal, chi-square, t-Student.
b) relations between some distributions

4. Samples of iid random variables
a) empirical distribution, histogram, box-plot
b) statistics of the sample: sample proportion, sample mean and sample variance
c) law of large numbers
d) central limit theorem
e) sample mean as random variable

IV. Statistical Inference

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

2. Hypothesis testing:
a) Errors of type I and type II, significance level
b) p-value of a test
c) relation between hypothesis testing and confidence intervals
d) parametric tests for the mean, variance and proportion

Mandatory literature

Rita Gaio; Apontamentos de "Matemática e Bioestatística"

Complementary Bibliography

M. Spivak; Calculus, Publish or Perish; fourth edition , 2008. ISBN: ISBN-13: 978-0914098911
J. Marsden, A. Weinstein; Calculus, Addison Wesley Longman, 2003. ISBN: 0-201-79131-5
W.W. Daniel; Biostatistics: a foundation for analysis in the health sciences, John Wiley and sons , 1999. ISBN: 0-471-16386-4
A.C. Pedrosa, S.M.A. Gama; Introdução Computacional à Probabilidade e Estatística, Porto Editora, 2004. ISBN: 972-0-06056-5

Teaching methods and learning activities

The classroom theoretical lectures are mainly devoted to the exposure and explanation of the matters. The process is carried out in a dynamical way and adjusted to the audience assimilation speed. Whenever possible, potential application examples will be given. 

 

The classroom theoretical/practical sessions will have a period in which students are encouraged to independently solve the proposed practical exercises, being that its resolution is always subsequently made and commented by the teacher. Use of the statistical packages available on the graphing calculators.

keywords

Physical sciences > Mathematics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	65,00
Participação presencial	0,00
Teste	35,00
Total:	100,00

Calculation formula of final grade

There will be a test about the Calculus component of the course mainly covering items I and II of the course program. The test is graded from 0 to 7, will last for 2 hours. In case the student prefers, there is no need to answer the corresponding questions on the final exam and the grade obtained in the test will be used for the corresponding part of the final exam.

 Final exam at "época normal"graded from 0 to 20, being that the grade 20 will only be given to the students that, besides having obtained 19.5 points, solve correctly an exercise of harder difficulty.

The exam at "época de recurso" is graded from 0 to 20 and does not take into account the classification that the student obtained in the first test. The students must solve the whole exam.