https://mklab.gr/ Sat, 12 Sep 2026 09:01:12 +0000 MyBB https://mklab.gr/showthread.php?tid=1100 Mon, 13 Jul 2026 18:50:02 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1100  Control Systems: An Introduction 
by Hassan K. Khalil

Summary

The textbook "Control Systems: An Introduction" by Professor Hassan Khalil of Michigan State University is intended to serve the standard course on control systems commonly required by undergraduate degrees in electrical and computer engineering. The book introduces the mathematical tools used to characterize the operation of a wide range of control systems, from those used to control a car to travel at a specified speed to a more elaborate systems used to  control the flight of a rocket. 

BOOK PAGE]]>  Control Systems: An Introduction 
by Hassan K. Khalil

Summary

The textbook "Control Systems: An Introduction" by Professor Hassan Khalil of Michigan State University is intended to serve the standard course on control systems commonly required by undergraduate degrees in electrical and computer engineering. The book introduces the mathematical tools used to characterize the operation of a wide range of control systems, from those used to control a car to travel at a specified speed to a more elaborate systems used to  control the flight of a rocket. 

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=964 Wed, 08 Jul 2026 18:39:08 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=964 Laboratories in Mathematical Experimentation 
BY [J. William Bruce]


Summary

Laboratories in Mathematical Experimentation: A Bridge to Higher Mathematics presents an innovative approach to learning mathematics by replacing passive study with active discovery. Designed for students who have completed calculus and are ready to transition into higher mathematics, the book consists of sixteen hands-on laboratory investigations that encourage experimentation, pattern recognition, conjecture, and proof. 

Rather than introducing abstract concepts through traditional lectures alone, the text invites readers to explore mathematical ideas with the aid of computer-based experimentation, helping them develop the intuition and critical thinking skills needed for advanced topics such as abstract algebra, geometry, number theory, and mathematical reasoning. Although many activities make use of computers, the material remains independent of any specific software, ensuring broad accessibility and flexibility.

The authors emphasize that mathematical experimentation is not merely a teaching technique but an essential part of how mathematics is explored and understood. By engaging with carefully designed investigations, students learn to ask meaningful questions, test hypotheses, recognize underlying structures, and construct rigorous arguments from their observations. This inquiry-based approach bridges the gap between computational mathematics and abstract thinking while fostering creativity, collaboration, and deeper conceptual understanding. 

Suitable for a one-semester sophomore-level course, the textbook reflects modern mathematics education by encouraging students to become active participants in the learning process rather than passive recipients of knowledge. Ultimately, the book demonstrates that experimentation is a powerful pathway to mastering higher mathematics and developing the analytical mindset that underpins mathematical research and problem-solving. 

BOOK (PDF)]]> Laboratories in Mathematical Experimentation 
BY [J. William Bruce]


Summary

Laboratories in Mathematical Experimentation: A Bridge to Higher Mathematics presents an innovative approach to learning mathematics by replacing passive study with active discovery. Designed for students who have completed calculus and are ready to transition into higher mathematics, the book consists of sixteen hands-on laboratory investigations that encourage experimentation, pattern recognition, conjecture, and proof. 

Rather than introducing abstract concepts through traditional lectures alone, the text invites readers to explore mathematical ideas with the aid of computer-based experimentation, helping them develop the intuition and critical thinking skills needed for advanced topics such as abstract algebra, geometry, number theory, and mathematical reasoning. Although many activities make use of computers, the material remains independent of any specific software, ensuring broad accessibility and flexibility.

The authors emphasize that mathematical experimentation is not merely a teaching technique but an essential part of how mathematics is explored and understood. By engaging with carefully designed investigations, students learn to ask meaningful questions, test hypotheses, recognize underlying structures, and construct rigorous arguments from their observations. This inquiry-based approach bridges the gap between computational mathematics and abstract thinking while fostering creativity, collaboration, and deeper conceptual understanding. 

Suitable for a one-semester sophomore-level course, the textbook reflects modern mathematics education by encouraging students to become active participants in the learning process rather than passive recipients of knowledge. Ultimately, the book demonstrates that experimentation is a powerful pathway to mastering higher mathematics and developing the analytical mindset that underpins mathematical research and problem-solving. 

BOOK (PDF)]]> https://mklab.gr/showthread.php?tid=963 Wed, 08 Jul 2026 18:35:13 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=963 Mathematics of Language 
by Marcus Kracht

Summary 

Mathematics of Language by Marcus Kracht offers a comprehensive introduction to mathematical linguistics, showing how mathematics, logic, and computer science provide powerful tools for understanding the structure and meaning of language. Rather than treating language simply as a collection of strings or sentences, the book presents it as a system of interconnected signs that combine form, syntax, and semantics. 
Starting with the foundations of set theory, algebra, formal grammars, automata, and computability, Kracht gradually builds a framework for analyzing how natural and formal languages are organized. He emphasizes that mathematical methods are not meant to replace linguistic theory but to clarify its assumptions, reveal hidden structures, and provide precise models for studying syntax, meaning, and language processing.
As the book progresses, it explores context-free languages, categorial grammar, formal semantics, Montague semantics, parsing algorithms, mildly context-sensitive grammars, and logical approaches to linguistic description. A central theme throughout is compositionality—the idea that the meaning of larger expressions arises systematically from the meanings of their parts and the rules used to combine them. Kracht also examines the computational complexity of natural language, the limitations of existing grammatical models, and the role of logic in describing linguistic structures with mathematical precision. 
By bringing together ideas from linguistics, mathematics, and theoretical computer science, the book demonstrates how rigorous formal methods deepen our understanding of human language and continue to influence fields such as computational linguistics, natural language processing, and artificial intelligence.


BOOK (PDF)]]> Mathematics of Language 
by Marcus Kracht

Summary 

Mathematics of Language by Marcus Kracht offers a comprehensive introduction to mathematical linguistics, showing how mathematics, logic, and computer science provide powerful tools for understanding the structure and meaning of language. Rather than treating language simply as a collection of strings or sentences, the book presents it as a system of interconnected signs that combine form, syntax, and semantics. 
Starting with the foundations of set theory, algebra, formal grammars, automata, and computability, Kracht gradually builds a framework for analyzing how natural and formal languages are organized. He emphasizes that mathematical methods are not meant to replace linguistic theory but to clarify its assumptions, reveal hidden structures, and provide precise models for studying syntax, meaning, and language processing.
As the book progresses, it explores context-free languages, categorial grammar, formal semantics, Montague semantics, parsing algorithms, mildly context-sensitive grammars, and logical approaches to linguistic description. A central theme throughout is compositionality—the idea that the meaning of larger expressions arises systematically from the meanings of their parts and the rules used to combine them. Kracht also examines the computational complexity of natural language, the limitations of existing grammatical models, and the role of logic in describing linguistic structures with mathematical precision. 
By bringing together ideas from linguistics, mathematics, and theoretical computer science, the book demonstrates how rigorous formal methods deepen our understanding of human language and continue to influence fields such as computational linguistics, natural language processing, and artificial intelligence.


BOOK (PDF)]]> https://mklab.gr/showthread.php?tid=569 Mon, 22 Jun 2026 11:04:19 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=569 Seeing circles, sines and signals, 
BY Jack Schaedler

Summary

Circles, Sines, and Signals by Jack Schaedler is an interactive visual introduction to digital signal processing (DSP) that explains the ideas behind sine waves, sampling, and the Discrete Fourier Transform (DFT) through animations, graphics, and sound rather than traditional equations alone. 

The tutorial builds intuition by showing how sine and cosine waves emerge from circular motion (phasors), how complex signals can be created by combining simple waves, and how Fourier analysis breaks signals into their frequency components. 

It also explores concepts such as continuous vs. discrete signals, correlation, phase, and reconstruction, helping readers understand why the Fourier Transform is so powerful in areas like audio processing, communications, and data analysis. 

BOOK PAGE]]> Seeing circles, sines and signals, 
BY Jack Schaedler

Summary

Circles, Sines, and Signals by Jack Schaedler is an interactive visual introduction to digital signal processing (DSP) that explains the ideas behind sine waves, sampling, and the Discrete Fourier Transform (DFT) through animations, graphics, and sound rather than traditional equations alone. 

The tutorial builds intuition by showing how sine and cosine waves emerge from circular motion (phasors), how complex signals can be created by combining simple waves, and how Fourier analysis breaks signals into their frequency components. 

It also explores concepts such as continuous vs. discrete signals, correlation, phase, and reconstruction, helping readers understand why the Fourier Transform is so powerful in areas like audio processing, communications, and data analysis. 

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=318 Sat, 13 Jun 2026 13:15:15 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=318 An Introduction to Statistical Signal Processing 
Robert M. Gray, Lee D. Davisson


Summary  This book describes the essential tools and techniques of statistical signal processing. At every stage theoretical ideas are linked to specific applications in communications and signal processing using a range of carefully chosen examples.

BOOK PAGE]]> An Introduction to Statistical Signal Processing 
Robert M. Gray, Lee D. Davisson


Summary  This book describes the essential tools and techniques of statistical signal processing. At every stage theoretical ideas are linked to specific applications in communications and signal processing using a range of carefully chosen examples.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=317 Sat, 13 Jun 2026 13:12:45 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=317 Foundations of Signal Processing 
Martin Vetterli, Jelena Kovacevic, Vivek K Goyal

Summary
This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica® resources and interactive demonstrations.

BOOK PAGE]]> Foundations of Signal Processing 
Martin Vetterli, Jelena Kovacevic, Vivek K Goyal

Summary
This comprehensive and engaging textbook introduces the basic principles and techniques of signal processing, from the fundamental ideas of signals and systems theory to real-world applications. Students are introduced to the powerful foundations of modern signal processing, including the basic geometry of Hilbert space, the mathematics of Fourier transforms, and essentials of sampling, interpolation, approximation and compression The authors discuss real-world issues and hurdles to using these tools, and ways of adapting them to overcome problems of finiteness and localization, the limitations of uncertainty, and computational costs. It includes over 160 homework problems and over 220 worked examples, specifically designed to test and expand students' understanding of the fundamentals of signal processing, and is accompanied by extensive online materials designed to aid learning, including Mathematica® resources and interactive demonstrations.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=274 Wed, 10 Jun 2026 23:15:56 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=274 Math in Society 

David Lippman

Summary 

"Math in Society" (edited and primarily authored by David Lippman) is a widely used, free, open-source textbook hosted on the University of Minnesota’s Open Textbook Library.
It is designed specifically as a survey of contemporary mathematical topics for liberal arts majors and other students taking a college-level quantitative literacy or general education mathematics course.

PAGE BOOK

]]> Math in Society 

David Lippman

Summary 

"Math in Society" (edited and primarily authored by David Lippman) is a widely used, free, open-source textbook hosted on the University of Minnesota’s Open Textbook Library.
It is designed specifically as a survey of contemporary mathematical topics for liberal arts majors and other students taking a college-level quantitative literacy or general education mathematics course.

PAGE BOOK

]]> https://mklab.gr/showthread.php?tid=272 Wed, 10 Jun 2026 22:59:51 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=272 Introduction to the Modeling and Analysis of Complex Systems
Author(s): Hiroki Sayama

Summary 

Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.

BOOK PAGE]]> Introduction to the Modeling and Analysis of Complex Systems
Author(s): Hiroki Sayama

Summary 

Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=256 Wed, 10 Jun 2026 03:59:57 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=256 Mathematics for the Physical Sciences
by Leslie Copley

Summary  A text on advanced mathematical methods with numerous applications, detailed derivations and solutions, and a unique range of practical topics. The book begins with a thorough introduction to complex analysis, which is then used to understand the properties of ordinary differential equations and their solutions. The latter are obtained in both series and integral representations. Integral transforms are introduced, providing an opportunity to complement complex analysis with techniques that flow from an algebraic approach. This moves naturally into a discussion of eigenvalue and boundary vale problems.

BOOK PAGE]]> Mathematics for the Physical Sciences
by Leslie Copley

Summary  A text on advanced mathematical methods with numerous applications, detailed derivations and solutions, and a unique range of practical topics. The book begins with a thorough introduction to complex analysis, which is then used to understand the properties of ordinary differential equations and their solutions. The latter are obtained in both series and integral representations. Integral transforms are introduced, providing an opportunity to complement complex analysis with techniques that flow from an algebraic approach. This moves naturally into a discussion of eigenvalue and boundary vale problems.

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=81 Wed, 03 Jun 2026 22:54:02 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=81 Title : An Introduction to Contemporary Mathematics
Author: John Hutchinson
Publisher: Australian National University 2010

Summary :  The goal is to introduce you to contemporary mainstream 20th and 21st century mathematics

BOOK PAGE]]> Title : An Introduction to Contemporary Mathematics
Author: John Hutchinson
Publisher: Australian National University 2010

Summary :  The goal is to introduce you to contemporary mainstream 20th and 21st century mathematics

BOOK PAGE]]> https://mklab.gr/showthread.php?tid=72 Mon, 01 Jun 2026 22:45:35 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=72 Εφαρμοσμένα Μαθηματικά
Υπότιτλος: Διαφορικές Εξισώσεις, Μιγαδικές Συναρτήσεις και Ολοκληρωτικοί Μετασχηματισμοί
Συγγραφείς: Τσίτσας, Νικόλαος

Το βιβλίο προσφέρει μια ενοποιημένη παρουσίαση των [b]Συνήθων Διαφορικών Εξισώσεων, των Μιγαδικών Συναρτήσεων και των Μετασχηματισμών Fourier, εστιάζοντας στις εφαρμογές τους στις φυσικές, τεχνολογικές επιστήμες και την Πληροφορική.
Η ύλη χωρίζεται σε τρία αντίστοιχα μέρη:[/b]

• [b]Συνήθεις Διαφορικές Εξισώσεις: Μελέτη ύπαρξης λύσεων (καθαρά Μαθηματικά), μεθοδολογίες υπολογισμού τους (εφαρμοσμένα Μαθηματικά) και χρήση τους στη μαθηματική μοντελοποίηση.[/b]
  
• [b]Μιγαδικές Συναρτήσεις: Παρουσίαση ισχυρών τεχνικών και εργαλείων που χρησιμοποιούνται για τη μοντελοποίηση εφαρμογών σε άλλες επιστήμες.[/b]
  
• [b]Σειρές και Μετασχηματισμοί Fourier: Ολοκληρωτική αναπαράσταση συναρτήσεων και η χρήση τους για τη μετάβαση από το πεδίο του χρόνου/χώρου στο πεδίο των συχνοτήτων.[/b]
  

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SOURCE]]> Εφαρμοσμένα Μαθηματικά
Υπότιτλος: Διαφορικές Εξισώσεις, Μιγαδικές Συναρτήσεις και Ολοκληρωτικοί Μετασχηματισμοί
Συγγραφείς: Τσίτσας, Νικόλαος

Το βιβλίο προσφέρει μια ενοποιημένη παρουσίαση των [b]Συνήθων Διαφορικών Εξισώσεων, των Μιγαδικών Συναρτήσεων και των Μετασχηματισμών Fourier, εστιάζοντας στις εφαρμογές τους στις φυσικές, τεχνολογικές επιστήμες και την Πληροφορική.
Η ύλη χωρίζεται σε τρία αντίστοιχα μέρη:[/b]

• [b]Συνήθεις Διαφορικές Εξισώσεις: Μελέτη ύπαρξης λύσεων (καθαρά Μαθηματικά), μεθοδολογίες υπολογισμού τους (εφαρμοσμένα Μαθηματικά) και χρήση τους στη μαθηματική μοντελοποίηση.[/b]
  
• [b]Μιγαδικές Συναρτήσεις: Παρουσίαση ισχυρών τεχνικών και εργαλείων που χρησιμοποιούνται για τη μοντελοποίηση εφαρμογών σε άλλες επιστήμες.[/b]
  
• [b]Σειρές και Μετασχηματισμοί Fourier: Ολοκληρωτική αναπαράσταση συναρτήσεων και η χρήση τους για τη μετάβαση από το πεδίο του χρόνου/χώρου στο πεδίο των συχνοτήτων.[/b]
  

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SOURCE]]>