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"This book is a short primer in engineering mathematics with a view on applications in nonlinear control theory. In particular, it introduces some elementary concepts of commutative algebra and algebraic geometry which offer a set of tools quite different from the traditional approaches to the subject matter.This text begins with the study of elementary set and map theory. Chapters 2 and 3 on group theory and rings, respectively, are included because of their important relation to linear algebra, the group of invertible linear maps (or matrices) and the ring of linear maps of a vector space. Homomorphisms and Ideals are dealt with as well at this stage. Chapter 4 is devoted to the theory of matrices and systems of linear equations. Chapter 5 gives some information on permutations, determinants and the inverse of a matrix. Chapter 6 tackles vector spaces over a field, Chapter 7 treats linear maps resp. linear transformations, and in addition the application in linear control theory of some abstract theorems such as the concept of a kernel, the image and dimension of vector spaces are illustrated. Chapter 8 considers the diagonalization of a matrix and their canonical forms. Chapter 9 provides a brief introduction to elementary methods for solving differential equations and, finally, in Chapter 10, nonlinear control theory is introduced from the point of view of differential algebra. "

"Aljabar max-plus merupakan sebuah aljabar yang banyak diterapkan dalam berbagai bidang, terutama permasalahan optimisasi. Sebagaimana pada ruang Euclid, konsep geometri seperti semiruang dan hiperbidang juga dapat diterapkan pada aljabar max-plus. Terdapat beberapa perbedaan dari semiruang dan hiperbidang pada aljabar max-plus dengan semiruang dan hiperbidang pada ruang Euclid. Perbedaan ini muncul karena aljabar max-plus memiliki operasi yang berbeda. Pada skripsi ini, dipelajari aspek geometri dari aljabar max-plus terutama pada semiruang dan hiperbidang. Selanjutnya dipelajari pula keterkaitan di antara komplemen semiruang dan hiperbidang.

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The max-plus algebra is an algebra which is used in many subjects, especially optimization problem. Similar with the Euclid space, some geometrical concept such as semispaces and hyperplanes can be defined in max-plus algebra. There are some differences between semispaces and hyperplanes in max-plus algebra and semispaces and hyperplanes in the Euclid space. These differences occur because the max-plus algebra has different operations. In this undergraduate thesis, some characteristic of semispace and hyperplane will be studied. Furthermore, the relation between complement semispaces and hyperplanes will also be studied."