This book introduces readers to the art of doing mathematical proofs. Proofs are the glue that holds mathematics together. They make connections between math concepts and show why things work the way they do. This book teaches the art of proofs using familiar high school concepts, such as numbers, polynomials, functions, and trigonometry. It retells math as a story, where the next chapter follows from the previous one. Readers will see how various mathematical concepts are tied, will see mathematics is (...) not a pile of formulas and facts, but has an orderly and beautiful edifice. The author begins with basic rules of logic, and then progresses through the topics already familiar to the students: numbers, inequalities, functions, polynomials, exponents, and trigonometric functions. There are also beautiful proofs for conic sections, sequences, and Fibonacci numbers. Each chapter has exercises for the reader. (shrink)

The paper aims to analyze the scope of female leadership (deanship) at public and non-public law faculties in selected countries from the region of Central and Eastern Europe: Poland, Hungary, Czechia, Slovakia, Lithuania, Latvia, Estonia, Bulgaria, Romania, Slovenia, Croatia, Serbia, Kosovo, Bosnia and Hercegovina, Montenegro. The paper will explore the engagement of women in the administration of law schools operating within public (and non-public) schools (universities) across the region in the latest years. The paper aims to show the number of (...) female deanships at law faculties in the analyzed states. This analysis will be based on statistical data obtained from the available public sources (including national databases as well as the European Union resources) providing the number of female deans and vice-deans appointed or elected by the academia at all higher education institutions within the country. The initial hypothesis states that gender inequality has been present in the deanship of analyzed law schools and reflects general trends in gender equality in Europe. Comprehensive analysis of the central and eastern European states will allow formulating the key conclusions and answering the following research questions concerning the differences in the numbers of women on the key positions within the law faculties in terms of public versus non-public institutions and in the light of the general gender equality trends in the continent. The research methods used for the analysis include a dogmatic method, statistical method as well as comparative method. (shrink)