Engineering mathematics subject guide 

Mathematical Statistics provides a rigorous introduction to the theoretical foundations of statistical inference, focusing on the development and application of probability models to analyze data. The book begins with core concepts in probability and distributions, then builds toward sampling distributions that underpin statistical reasoning. It presents key techniques for point estimation and interval estimation, enabling readers to infer population parameters from sample data, and develops formal methods of hypothesis testing, including the use of critical regions and p-values, even in non-standard (skewed) distributions. Supporting appendices extend the discussion with essential statistical distributions, unified expectation methods, and computational algorithms such as Newton–Raphson and Fisher scoring. Overall, the text integrates theory and methodology to equip readers with the mathematical tools needed for sound statistical analysis and inference.

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Advanced Engineering Mathematics with MATLAB® offers a comprehensive treatment of the mathematical methods essential for engineering analysis, combining theoretical development with practical computational techniques. The text covers key topics including ordinary differential equations, linear algebra, and vector calculus before advancing to powerful analytical tools such as Fourier series, Fourier and Laplace transforms. It applies these methods to classical partial differential equations, including the wave, heat, and Laplace equations, demonstrating their relevance to real-world physical systems. The book also explores Sturm–Liouville theory and special functions, providing deeper insight into boundary-value problems. Throughout, MATLAB® is integrated to support numerical computation and visualization, enabling readers to bridge analytical solutions with modern computational practice.

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Advanced Mathematics for Engineers and Scientists with Worked Examples provides a structured and practice-oriented introduction to core mathematical techniques required in engineering and scientific disciplines. The book progresses from foundational topics such as trigonometric functions, identities, and equations to algebraic methods including binomial expansion and partial fractions, before developing more advanced concepts like complex numbers, matrices, and vectors. It then offers a comprehensive treatment of calculus, covering differentiation, integration (both basic and advanced), and their practical applications. Emphasising worked examples throughout, the text is designed to reinforce understanding and build problem-solving skills, enabling readers to apply mathematical methods confidently to real-world scientific and engineering problems.

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Everyday Cryptography: Fundamental Principles and Applications provides a clear and accessible introduction to the role of cryptography in securing modern digital systems. The book explains the fundamental principles underlying information security, including confidentiality, integrity, and authentication, before introducing key cryptographic tools such as encryption, hash functions, digital signatures, and authentication protocols. It emphasises practical understanding over complex mathematics, showing how these techniques are applied in real-world technologies like the internet, mobile communications, and payment systems. The text also explores crucial implementation issues such as key management and system design, and examines broader applications and societal implications of cryptography, including privacy and cybersecurity. Overall, it equips readers with both conceptual understanding and practical insight into how cryptography protects everyday digital interactions.

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Modern Statistics with R: From Wrangling and Exploring Data to Inference and Predictive Modelling provides a comprehensive introduction to contemporary statistical analysis using the R programming language, integrating data handling, theory, and computation. The book guides readers through the full data analysis workflow, beginning with data wrangling and exploratory data analysis, then developing core statistical inference techniques such as hypothesis testing and confidence intervals. It progresses to modern modelling approaches, including regression and machine learning methods for prediction and classification, alongside simulation techniques for evaluating statistical procedures. Emphasising practical application, reproducible analysis, and ethical considerations, the text equips readers with both conceptual understanding and hands-on programming skills needed to analyse complex data and build predictive models in real-world contexts.

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Quantum Computing: A Journey Into the Next Frontier of Information and Communication Security provides a comprehensive and accessible introduction to the rapidly evolving field of quantum computing, with a strong focus on its implications for cybersecurity and information systems. The book begins by explaining the foundational principles of quantum mechanics and quantum computing, then progresses to key concepts such as quantum algorithms, programming, and communication. It highlights both the transformative potential and the risks of quantum technologies, particularly their impact on current cryptographic systems, and explores solutions including quantum-safe cryptography, quantum key distribution, and emerging security standards. Emphasising practical applications and real-world adoption, the text equips readers with the knowledge needed to understand, evaluate, and prepare for the challenges and opportunities of the quantum era in digital security and data processing.

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Mathematical Formulas and Scientific Data: A Quick Reference Guide is a concise and practical compendium of essential mathematical expressions, constants, and scientific data designed for quick consultation. Covering a wide range of topics—including algebra, trigonometry, calculus, geometry, and key physical and scientific constants—the book provides readily accessible formulas and reference tables to support problem-solving and analysis in scientific and engineering contexts. Its structured layout prioritises clarity and efficiency, enabling students, researchers, and professionals to quickly locate critical information without extended theoretical discussion. Overall, the guide serves as a convenient reference tool to support learning, revision, and application of core mathematical and scientific principles.

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Engineering Simulation and Its Applications: Algorithms and Numerical Methods presents a comprehensive overview of the numerical techniques and computational algorithms used to model and simulate complex engineering systems. The book introduces fundamental concepts in simulation, focusing on how mathematical models are translated into numerical solutions through methods such as discretisation, iterative algorithms, and approximation techniques. It explores a range of applications across engineering disciplines, demonstrating how simulation can be used to analyse physical phenomena, optimise system performance, and support design decisions. Emphasising both theoretical foundations and practical implementation, the text equips readers with the tools needed to develop, evaluate, and apply simulation methods effectively in real-world engineering contexts.

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Mathematical Methods Using Python: Applications in Physics and Engineering introduces key mathematical techniques used in scientific and engineering analysis, integrating them with practical implementation using Python. The book covers core topics such as linear algebra, differential equations, numerical methods, and mathematical modelling, demonstrating how these tools are applied to solve real problems in physics and engineering. It emphasises computational approaches, showing how Python can be used to perform calculations, simulate systems, and visualise results, thereby bridging the gap between theory and practice. Through a combination of mathematical explanation and coding examples, the text equips readers with both the analytical understanding and programming skills needed to tackle complex, real-world problems efficiently.

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Introduction to Modern Scientific Programming and Numerical Methods provides a practical and accessible foundation for solving scientific and engineering problems through computational techniques. The book introduces core principles of scientific programming alongside essential numerical methods such as root finding, numerical integration, interpolation, and the solution of differential equations. It emphasises how mathematical problems are translated into algorithms and implemented in code, highlighting accuracy, efficiency, and error analysis. By integrating programming concepts with applied mathematics, the text enables readers to develop reliable computational solutions and understand the limitations of numerical approaches. Overall, it equips students and practitioners with the skills needed to apply modern programming tools to real-world scientific challenges.

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Provides information dealing with every theoretical, computational & applicational aspect of mathematical programming.

View Mathematical Programming (1999-present, 1 year delay)

A broad academic foundation for students and professionals interested in applying mathematical and computational techniques to real-world engineering and scientific problems.

View Quantum Topology (2021-present)

Covers areas of mathematical system theory, control theory and signal processing.

View Mathematics of Control, Signals, and Systems (1988-present, 1 year delay)

Published research papers and review articles in all areas of applied, computational, and industrial mathematics.

View the Journal of Applied Mathematics (2006-present)

Researches and surveys papers to better understand the connection between mathematics and computation.

View Foundations of Computational Mathematics (2001-present, 1 year delay)

IET Science, Measurement and Technology (fully open access journal)

IET Quantum Communication (fully open access journal)