ELEMENTI DI MATEMATICA E STATISTICA - FISICA

Module ELEMENTI DI MATEMATICA E STATISTICA

By the end of the course, students will have acquired an integrated understanding of the basic mathematical and

statistical tools needed to describe, analyse and interpret quantitative problems in Pharmaceutical Sciences. They will

be able to translate simple applications into relations, functions, models and statistical procedures, selecting

appropriate methods and representations.

Knowledge and understanding

• Understand set and logical language, number systems, ratios, percentages, scientific notation and orders of

magnitude.

• Know elementary algebra, equations and inequalities, powers, radicals, exponential and logarithmic functions.

• Understand functions, graphs, limits, continuity, derivatives, integrals and elementary differential equations.

• Know the foundations of descriptive statistics, probability, random variables, distributions and statistical inference.

Applying knowledge and understanding

• Solve quantitative problems involving concentrations, dilutions, dosage, percentages, pH, decay and half-life.

• Analyse functions and interpret rates of change, areas and elementary dynamic models.

• Organise experimental data and interpret descriptive indices, probabilities, confidence intervals and basic hypothesis

tests.

• Critically read tables and graphs and distinguish association, variability, uncertainty and statistical significance.

Making judgements

Students will assess the plausibility of results, recognise assumptions and limitations, identify scale or unit errors, and

select statistical summaries appropriate to the data.

Communication skills

Students will clearly present methods, notation, results and interpretations using appropriate graphs, units and

terminology.

Learning skills

and statistical study.

Students will develop an autonom

Lectures combine progressive explanations, guided examples and exercises. Numerical, algebraic and graphical

representations are consolidated through integrated pharmaceutical applications, self-assessment and discussion of

common errors.

If teaching is delivered in blended or remote mode, the necessary organisational changes may be introduced while

respecting the syllabus and stated learning outcomes.

Secondary-school mathematics: arithmetic, fractions, percentages, simple algebraic expressions, Cartesian

coordinates and elementary reading of tables and graphs. Essential prerequisites will be reviewed. No prior

university-level statistics is required.

Attendance is governed by the Degree Programme regulations. Regular participation is strongly recommended,

especially for exercises and applied activities.

1. Sets and logic

Propositions, connectives and truth tables; implication; sets and subsets; union, intersection, difference and

complement; Venn diagrams; intervals.

2. Numbers, ratios, percentages and scientific notation

Number systems; fractions; ratios; percentages; units and conversions; significant figures; orders of magnitude.

3. Algebra, equations and inequalities

Expressions; factorisation; linear and quadratic equations; elementary systems; inequalities and solution sets.

4. Powers, radicals, exponentials and logarithms

Laws of powers; radicals; exponential and logarithmic functions and equations; logarithmic scales and pH.

5. Analytic geometry and functions

Cartesian plane; line and parabola; domain, codomain and range; zeros and sign; polynomial, rational, exponential

and logarithmic functions; graphs.

6. Limits and continuity

Finite and infinite limits; elementary indeterminate forms; asymptotes; continuity and discontinuities; graphical

interpretation.

7. Derivatives and function analysis

Difference quotient; geometric meaning; differentiation rules; monotonicity, extrema, concavity, inflection points and

elementary optimisation.

8. Integrals

Antiderivatives; definite integrals as signed area and accumulation; fundamental theorem; elementary methods;

concentration-time area and AUC.

9. Elementary differential equations

First-order separable equations; exponential growth and decay; elementary initial-value problems; drug elimination

and half-life.

10. Descriptive statistics

Population, sample and variables; measurement scales; frequency tables and graphs; centre, quantiles, variance,

standard deviation, coefficient of variation and outliers.

11. Probability

Events and axioms; unions and intersections; conditional probability; independence; Bayes’ theorem; sensitivity,

specificity and predictive values.

12. Random variables and distributions

Discrete and continuous variables; expectation and variance; Bernoulli, binomial, Poisson, uniform and normal

distributions; standardisation.

13. Statistical inference

Sampling distributions; standard error; estimates and confidence intervals; null and alternative hypotheses; type I/II

errors, p-values and power; basic tests; introductory correlation and regression.

14. Integrated pharmaceutical applications

Dilution and dosage; pH; decay, half-life and pharmacokinetics; dose-response, Emax/EC50 and AUC; experimental

data and group comparisons.

• Teaching materials, slides, formula sheets and exercises provided by the teacher.

• Any additional references and resources will be communicated during the course.

Learning Assessment Procedures

The examination is a written test, subject to prior registration. It assesses conceptual knowledge and the ability to set

up, solve and interpret problems. It may include multiple-choice items, short answers, numerical exercises, and

interpretation of graphs or tables. Instructions specify duration, scoring and permitted materials.

Assessment considers correctness of method and result, appropriate use of notation and units, justification of steps,

and interpretation in mathematical, statistical or pharmaceutical context. The mark is expressed out of thirty; the pass

mark is 18/30. Honours may be awarded for full mastery, rigorous reasoning, autonomous connections and correct

critical interpretation.

Examples of Frequently Asked Questions and/or Exercises

The following illustrate question types consistent with the learning outcomes; numerical data and wording may vary

between examination sessions.

• Represent two sets with a Venn diagram and determine union, intersection, difference and complement.

• Prepare 250 mL of a 2% solution from a 10% stock solution.

• Write 0.000045 in scientific notation and state its order of magnitude.

• Solve a quadratic equation and a rational inequality, showing the solution set.

• Solve an exponential and a logarithmic equation, stating domain conditions.

• Determine domain, intercepts and sign of a rational function and sketch its graph.

• Compute a limit and identify any vertical or horizontal asymptote.

• Use a derivative to find monotonicity intervals and relative extrema.

• Compute a definite integral and interpret AUC in a concentration-time profile.