Browsing by Author "Khemis , Rabah"

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    MATHEMATICS 1 : First Semester For first year university students in matter sciences and related disciplines
    (Faculty of sciences, 2024-02) Khemis , Rabah
    Mathematics can be deemed as the language of science and technology due to the fact that the mathematical concepts and tools form integral parts of the vocabulary of several scholars working in various fields. For this, a knowledge of some basic mathematical concepts and techniques is crucial for an increasing number of university courses for a wide range of scientific disciplines such as mathematics, physics, chemistry, computer sciences, engineering and life sciences. Indeed, for physics and chemistry, mathematics has always been, and still is, one of the core tools since it promotes rigorous thinking, problem solving ability and help in expressing ideas, formulating theories, modelling and also getting a better understanding of a broad range of phenomena that appear almost in every facet of our lives. The red thread of this course which can be considered as a first step towards further learning in mathematics, is to introduce some basic mathematical concepts that are assumed to be mastered by students in chemistry and physics. Most of them are presented in their simplest but rigorous forms so that students that take their first steps in the university can easily understand them especially those with little background in mathematics and often no motivation to learn more. This course is not proof-based but it provides a scaffolded approach to learning main ideas and notions that will be required for applying mathematics in physics and chemistry. Whist it has been geared primarily towards first year students at the universities whose speciality is precisely matter sciences, the actual audience may be all students studying mathematics at the university whatever their speciality. Students are assumed to have a little prior knowledge especially knowledge of high school mathematics which should be a sufficient prerequisite. Furthermore, an acquaintance with some basic concepts of mathematical logic and some types of mathematical proof is an element of the knowledge required for this module. The content here is divided into two main parts: The first part that is made up of three chapters, deals with analysis whereas the second one is algebra. The first three chapters cover a collection of topics such as sets, relations and functions while the other three chapters focus on groups, rings, fields, vector spaces and linear transformations Finally, it is our aspiration that this course will greatly simplify the work of the students and will also be a helpful resource for them - including those struggling with their mathematics.