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Lectures on Applications-Oriented Mathematics
Meets the need for a program of short courses involving the essentials of a number of mathematical topics taken by physics and engineering students. Basically applications-oriented, the courses do include selected topics of abstract mathematics. While several courses can be used as practical appendices to conventional mathematics, others serve as introductions, providing motivation for self-study in areas of conceptual math.
R 7,358.00
R 555.50
Probability and Statistics for Data Science
This self-contained guide introduces two pillars of data science, probability theory, and statistics, side by side, in order to illuminate the connections between statistical techniques and the probabilistic concepts they are based on. The topics covered in the book include random variables, nonparametric and parametric models, correlation, estimation of population parameters, hypothesis testing, principal component analysis, and both linear and nonlinear methods for regression and classification. Examples throughout the book draw from real-world datasets to demonstrate concepts in practice and confront readers with fundamental challenges in data science, such as overfitting, the curse of dimensionality, and causal inference. Code in Python reproducing these examples is available on the book's website, along with videos, slides, and solutions to exercises. This accessible book is ideal for undergraduate and graduate students, data science practitioners, and others interested in the theoretical concepts underlying data science methods.
R 2,697.51
R 762.00
Applied Mathematics: Body and Soul
Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level. The authors are leading researchers in Computational Mathematics who have written various successful books.
R 2,582.69
Linear Programming: Mathematics, Theory and Algorithms
Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.
R 6,035.38
R 611.00
R 764.00
R 519.00
Non-Programmers Tutorial For Python 2 and 3
This book is a tutorial for the Python 2 and 3 programming language designed for someone with no programming experience. All the examples work in Python 2.6 and Python 3.
R 414.02
R 580.00
Computer-Based Mathematics Education and the Use of MatCos Software in Primary and Secondary Schools
The theme of inserting new digital technologies into the teaching and learning of mathematics from primary and secondary schools has provoked a wide and interesting debate. One such debate is the reformation of the foundations of mathematics to include computation (what and how to calculate) among the traditional themes (Arithmetic, Geometry, etc.) of mathematics. Thus, the authors propose the MatCos Project as a new approach for solving this issue. Computer-Based Mathematics Education and the Use of MatCos Software in Primary and Secondary Schools is a critical reference source that proposes a new pedagogical-learning paradigm that guides students in the formation of an active, logical-sequential, intuitive, and creative thinking that directs them towards problem-solving and starts students with computational thinking and programming in a natural way. The content of the book is divided into two parts, with the first exploring theoretical and pedagogical notes on mathematics and the second examining the MatCos programming environment and its systematic inclusion in teaching practice. Highlighting themes that include computer-assisted instruction, teaching-learning sequences, and programming, this book is ideal for in-service teachers, mathematics instructors, academicians, researchers, and students.
R 8,376.84
50 Algorithms Every Programmer Should Know
Delve into the realm of generative AI and large language models (LLMs) while exploring modern deep learning techniques, including LSTMs, GRUs, RNNs with new chapters included in this 50% new edition overhaulPurchase of the print or Kindle book includes a free eBook in PDF format.Key FeaturesFamiliarize yourself with advanced deep learning architecturesExplore newer topics, such as handling hidden bias in data and algorithm explainabilityGet to grips with different programming algorithms and choose the right data structures for their optimal implementationBook DescriptionThe ability to use algorithms to solve real-world problems is a must-have skill for any developer or programmer. This book will help you not only to develop the skills to select and use an algorithm to tackle problems in the real world but also to understand how it works.You'll start with an introduction to algorithms and discover various algorithm design techniques, before exploring how to implement different types of algorithms, with the help of practical examples. As you advance, you'll learn about linear programming, page ranking, and graphs, and will then work with machine learning algorithms to understand the math and logic behind them.Case studies will show you how to apply these algorithms optimally before you focus on deep learning algorithms and learn about different types of deep learning models along with their practical use.You will also learn about modern sequential models and their variants, algorithms, methodologies, and architectures that are used to implement Large Language Models (LLMs) such as ChatGPT.Finally, you'll become well versed in techniques that enable parallel processing, giving you the ability to use these algorithms for compute-intensive tasks.By the end of this programming book, you'll have become adept at solving real-world computational problems by using a wide range of algorithms.What you will learnDesign algorithms for solving complex problemsBecome familiar with neural networks and deep learning techniquesExplore existing data structures and algorithms found in Python librariesImplement graph algorithms for fraud detection using network analysisDelve into state-of-the-art algorithms for proficient Natural Language Processing illustrated with real-world examplesCreate a recommendation engine that suggests relevant movies to subscribersGrasp the concepts of sequential machine learning models and their foundational role in the development of cutting-edge LLMsWho this book is forThis computer science book is for programmers or developers who want to understand the use of algorithms for problem-solving and writing efficient code.Whether you are a beginner looking to learn the most used algorithms concisely or an experienced programmer looking to explore cutting-edge algorithms in data science, machine learning, and cryptography, you'll find this book useful.Python programming experience is a must, knowledge of data science will be helpful but not n
R 1,628.00
Mathematical Programming and Financial Objectives for Scheduling Projects
Mathematical Programming and Financial Objectives for Scheduling Projects focuses on decision problems where the performance is measured in terms of money. As the title suggests, special attention is paid to financial objectives and the relationship of financial objectives to project schedules and scheduling. In addition, how schedules relate to other decisions is treated in detail. The book demonstrates that scheduling must be combined with project selection and financing, and that scheduling helps to give an answer to the planning issue of the amount of resources required for a project. The author makes clear the relevance of scheduling to cutting budget costs. The book is divided into six parts. The first part gives a brief introduction to project management. Part two examines scheduling projects in order to maximize their net present value. Part three considers capital rationing. Many decisions on selecting or rejecting a project cannot be made in isolation and multiple projects must be taken fully into account. Since the requests for capital resources depend on the schedules of the projects, scheduling taken on more complexity. Part four studies the resource usage of a project in greater detail. Part five discusses cases where the processing time of an activity is a decision to be made. Part six summarizes the main results that have been accomplished.
R 1,539.89
R 1,373.00
AI and ML for Coders in Pytorch
Eager to learn AI and machine learning but unsure where to start? Laurence Moroney's hands-on, code-first guide demystifies complex AI concepts without relying on advanced mathematics. Designed for programmers, it focuses on practical applications using PyTorch, helping you build real-world models without feeling overwhelmed.From computer vision and natural language processing (NLP) to generative AI with Hugging Face Transformers, this book equips you with the skills most in demand for AI development today. You'll also learn how to deploy your models across the web and cloud confidently.Gain the confidence to apply AI without needing advanced math or theory expertiseDiscover how to build AI models for computer vision, NLP, and sequence modeling with PyTorchLearn generative AI techniques with Hugging Face Diffusers and Transformers
R 1,824.00
Applied Mathematics: Body and Soul
Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level. The authors are leading researchers in Computational Mathematics who have written various successful books.
R 1,583.84
Fuzzy Relational Mathematical Programming
This book summarizes years of research in the field of fuzzy relational programming, with a special emphasis on geometric models. It discusses the state-of-the-art in fuzzy relational geometric problems, together with key open issues that must be resolved to achieve a more efficient application of this method. Though chiefly based on research conducted by the authors, who were the first to introduce fuzzy geometric problems, it also covers important findings obtained in the field of linear and non-linear programming. Thanks to its balance of basic and advanced concepts, and its wealth of practical examples, the book offers a valuable guide for both newcomers and experienced researcher in the fields of soft computing and mathematical optimization.
R 4,377.55
Mathematics Education Through Technology: Precalculus, Calculus, And More
This book caters to both prospective and current mathematics educators at the school and university levels, along with their students and anyone intrigued by the possibilities of integrating software into mathematics education.Mathematics, being a unified science, is best comprehended when its cohesive nature is emphasized and demonstrated to students. Educational software assumes a pivotal role in achieving this pedagogical goal.The book outlines the author's methodology in utilizing educational software for developing and applying computer models, grounded in a thorough analysis of the subject matter. This approach is vividly illustrated through examples employing a non-profit authoring program (VisuMatica) provided with the book, enabling users to:Through the guidance of this book, students will discover mathematics as clear, visible, friendly, and enjoyable.The author exemplifies this approach by focusing on the functional line of mathematics, spanning from school basics to advanced university courses in higher mathematics. Importantly, the assimilated ideas and techniques are readily applicable to teaching and learning other areas of mathematics.
R 5,788.00
R 317.00
Bird's Basic Engineering Mathematics
Now in its eighth edition, Bird’s Basic Engineering Mathematics has helped thousands of students to succeed in their exams. Mathematical theories are explained in a straightforward manner, supported by practical engineering examples and applications to ensure that readers can relate theory to practice. Some 1,000 engineering situations/problems have been ‘flagged-up’ to help demonstrate that engineering cannot be fully understood without a good knowledge of mathematics.The extensive and thorough coverage makes this a great text for introductory level engineering courses – such as for aeronautical, construction, electrical, electronic, mechanical, manufacturing engineering and vehicle technology – including for BTEC First, National and Diploma syllabuses, City & Guilds Technician Certificate and Diploma syllabuses, and even for GCSE revision.Its companion website provides extra materials for students and lecturers, including full solutions for all 1,700 further questions, lists of essential formulae, multiple choice tests, and illustrations, as well as full solutions to revision tests for course instructors.
R 2,161.00
Mathematics of Nonlinear Programming
Nonlinear programming provides an excellent opportunity to explore an interesting variety of pure and solidly applicable mathematics, numerical analysis, and computing. This text develops some of the ideas and techniques involved in the optimization methods using calculus, leading to the study of convexity. This is followed by material on basic numerical methods, least squares, the Karush-Kuhn-Tucker theorem, penalty functions, and Lagrange multipliers. The authors have aimed their presentation at the student who has a working knowledge of matrix algebra and advanced calculus, but has had no previous exposure to optimization.
R 2,496.74
Mathematics for Artificial Intelligence
Artificial intelligence (AI) and machine learning (ML) are rapidly growing fields drawing great interest among students. Many students in a range of fields, including mathematics, computer science, statistics, data science, and more, see AI and ML as a key to their future.This book provides the basic mathematics needed to understand AI and ML. It serves both students of mathematics and those who want to fill any gaps in their mathematics experience. It is written as both a text for a course and as a focused look at mathematics needed for readers hoping to learn more.The author has taught every topic in this book, often in different contexts, and the material and exercises are drawn from lecture notes. The material in the book represents a curated set of topics from the undergraduate math curriculum, some first-year seminar material, and some student project topics. Through carefully chosen examples and discussion in the text, the reader will learn how and where these tools are applied. AI and ML connections are raised along the way.It presumes the reader has at least completed the traditional three-semester calculus course. Linear algebra is presented as needed and should not require a completed course. The book is also well-suited for self-paced learning. Each chapter can be read independently with the help of the index for cross-referencing. Exercises are included.
R 2,988.69
Mathematical Introduction to Linear Programming and Game Theory
Mathematical elegance is a constant theme in this treatment of linear programming and matrix games. Condensed tableau, minimal in size and notation, are employed for the simplex algorithm. In the context of these tableau the beautiful termination theorem of R.G. Bland is proven more simply than heretofore, and the important duality theorem becomes almost obvious. Examples and extensive discussions throughout the book provide insight into definitions, theorems, and applications. There is considerable informal discussion on how best to play matrix games. The book is designed for a one-semester undergraduate course. Readers will need a degree of mathematical sophistication and general tools such as sets, functions, and summation notation. No single college course is a prerequisite, but most students will do better with some prior college mathematics. This thorough introduction to linear programming and game theory will impart a deep understanding of the material and also increase the student's mathematical maturity.
R 1,531.82
R 671.00
R 305.00
Python Network Programming
Power up your network applications with Python programmingKey FeaturesMaster Python skills to develop powerful network applicationsGrasp the fundamentals and functionalities of SDNDesign multi-threaded, event-driven architectures for echo and chat serversBook DescriptionThis Learning Path highlights major aspects of Python network programming such as writing simple networking clients, creating and deploying SDN and NFV systems, and extending your network with Mininet. You’ll also learn how to automate legacy and the latest network devices. As you progress through the chapters, you’ll use Python for DevOps and open source tools to test, secure, and analyze your network. Toward the end, you'll develop client-side applications, such as web API clients, email clients, SSH, and FTP, using socket programming.By the end of this Learning Path, you will have learned how to analyze a network's security vulnerabilities using advanced network packet capture and analysis techniques. This Learning Path includes content from the following Packt products:Practical Network Automation by Abhishek RatanMastering Python Networking by Eric ChouPython Network Programming Cookbook, Second Edition by Pradeeban Kathiravelu, Dr. M. O. Faruque SarkerWhat you will learnCreate socket-based networks with asynchronous modelsDevelop client apps for web APIs, including S3 Amazon and TwitterTalk to email and remote network servers with different protocolsIntegrate Python with Cisco, Juniper, and Arista eAPI for automationUse Telnet and SSH connections for remote system monitoringInteract with websites via XML-RPC, SOAP, and REST APIsBuild networks with Ryu, OpenDaylight, Floodlight, ONOS, and POXConfigure virtual networks in different deployment environmentsWho this book is forIf you are a Python developer or a system administrator who wants to start network programming, this Learning Path gets you a step closer to your goal. IT professionals and DevOps engineers who are new to managing network devices or those with minimal experience looking to expand their knowledge and skills in Python will also find this Learning Path useful. Although prior knowledge of networking is not required, some experience in Python programming will be helpful for a better understanding of the concepts in the Learning Path.
R 1,628.00
Python for Data Analysis 3e
Get the definitive handbook for manipulating, processing, cleaning, and crunching datasets in Python. Updated for Python 3.10 and pandas 1.4, the third edition of this hands-on guide is packed with practical case studies that show you how to solve a broad set of data analysis problems effectively. You'll learn the latest versions of pandas, NumPy, and Jupyter in the process.Written by Wes McKinney, the creator of the Python pandas project, this book is a practical, modern introduction to data science tools in Python. It's ideal for analysts new to Python and for Python programmers new to data science and scientific computing. Data files and related material are available on GitHub.Use the Jupyter notebook and IPython shell for exploratory computingLearn basic and advanced features in NumPyGet started with data analysis tools in the pandas libraryUse flexible tools to load, clean, transform, merge, and reshape dataCreate informative visualizations with matplotlibApply the pandas groupby facility to slice, dice, and summarize datasetsAnalyze and manipulate regular and irregular time series dataLearn how to solve real-world data analysis problems with thorough, detailed examples
R 1,978.00
R 794.00
Programming: A Primer - Coding For Beginners
Have you ever wanted to learn how to program but never found quite the right book to get you started? Programming: A Primer gets you going straight away with the fundamentals of what programming is, basic programming with Python and the fundamental aspects of practical web development. In this book, you'll learn about:Programming: A Primer offers an easy way into coding for anyone with an interest in using technology to solve problems, whether a school or new undergraduate computer science student or a working professional. It gives everyone, regardless of background, the ideal foundations and motivation needed to get to grips with programming.A companion website can be found here: .
R 1,163.84
Mathematical Programming and Financial Objectives for Scheduling Projects
Mathematical Programming and Financial Objectives for Scheduling Projects focuses on decision problems where the performance is measured in terms of money. As the title suggests, special attention is paid to financial objectives and the relationship of financial objectives to project schedules and scheduling. In addition, how schedules relate to other decisions is treated in detail. The book demonstrates that scheduling must be combined with project selection and financing, and that scheduling helps to give an answer to the planning issue of the amount of resources required for a project. The author makes clear the relevance of scheduling to cutting budget costs. The book is divided into six parts. The first part gives a brief introduction to project management. Part two examines scheduling projects in order to maximize their net present value. Part three considers capital rationing. Many decisions on selecting or rejecting a project cannot be made in isolation and multiple projects must be taken fully into account. Since the requests for capital resources depend on the schedules of the projects, scheduling taken on more complexity. Part four studies the resource usage of a project in greater detail. Part five discusses cases where the processing time of an activity is a decision to be made. Part six summarizes the main results that have been accomplished.
R 1,540.07
Applied Mathematics Toolkit
Modern scientific and engineering systems are increasingly defined by nonlinearity, high dimensionality, partial observability, and uncertainty. Addressing such complexity requires more than isolated techniques. It calls for an integrated applied mathematics perspective that connects modeling, data analysis, and computation within a coherent framework. This book develops such a unified toolkit. Rather than treating mathematical methods as separate disciplines, it emphasizes their complementary roles in understanding, analyzing, and predicting complex systems, with a focus on intuition, practical relevance, and transferability across scientific and engineering fields.• It presents a broad collection of essential applied mathematics tools, organized to emphasize their interplay rather than treating them as isolated topics.• Each method is Introduced through simple yet illuminating examples that make advanced concepts accessible without sacrificing rigor.• For every technique, the presentation highlights the underlying motivation, key assumptions, strengths, limitations, and the contexts in which it is most effective.• Theory, data, and algorithms are consistently integrated to demonstrate how they work together in practical applications.• The book is accompanied by short “one concept- one example" videos, each 5-10 minutes long, focusing on a single idea and using deliberately simple examples to support initial exposure, intuition building, and efficient review.• Example codes are included to reinforce the concepts and facilitate hands-on learning.This book is intended for advanced undergraduate students, graduate students, and researchers in applied mathematics, science, and engineering who seek practical mastery of modern mathematical tools. It is well suited to topic courses and self-study, particularly for readers working at the intersection of modeling, data, and computation. By combining conceptual clarity with hands-on examples and an integrated methodology, the book provides a foundation for tackling real-world problems in a wide range of interdisciplinary settings.
R 6,960.00
Visual Studio Code for Python Programmers
Become proficient and efficient with Visual Studio Code and learn how to integrate all your external tools! Visual Studio Code for Python Programmers helps Python developers become not just familiar, but productive in Visual Studio Code. To start, you’ll find the steps for installing Visual Studio Code on Windows, Mac and Linux platforms, along with an introduction to the editing features of the workspace. Coverage of more advanced functionality includes managing source code, debugging, unit testing, and Jupyter Notebook support. The book finishes with a walk-through of real-world projects which utilize Visual Studio Code features introduced in the book. For developers, the choice of an editor is a very personal one. You have idiosyncratic needs and wants that are unique to you as a developer. This book will help you learn how to customize Visual Studio Code to meet your needs and Python development workflow. Introduces you to the features of the Visual Studio Code workspace and how those features can be customizedDemonstrates how Visual Studio Code allows you to choose your structure according to your needsCovers editing code in Python, including syntax highlighting, code completion, object definition, refactoring, and code navigationDescribes Git integration and how to perform common Git functions (commits, checkouts, branches, and merges) from within Visual Studio CodeHighlights debugging features for Python developers A final section on Real World Applications will step you through several examples (and features integration with Django, Flask, Jupyter Notebook, Docker, and Azure), so you can hit the ground running with Visual Studio Code.
R 1,140.00
Probability and Statistics for Data Science
This self-contained guide introduces two pillars of data science, probability theory, and statistics, side by side, in order to illuminate the connections between statistical techniques and the probabilistic concepts they are based on. The topics covered in the book include random variables, nonparametric and parametric models, correlation, estimation of population parameters, hypothesis testing, principal component analysis, and both linear and nonlinear methods for regression and classification. Examples throughout the book draw from real-world datasets to demonstrate concepts in practice and confront readers with fundamental challenges in data science, such as overfitting, the curse of dimensionality, and causal inference. Code in Python reproducing these examples is available on the book's website, along with videos, slides, and solutions to exercises. This accessible book is ideal for undergraduate and graduate students, data science practitioners, and others interested in the theoretical concepts underlying data science methods.
R 5,940.16
R 1,130.00
Python Illustrated
Learn Python coding concepts the fun way through humour, storytelling, and beginner-friendly examples that make your first step into the world of Python programming enjoyableKey FeaturesFollow an adorable, illustrated teaching cat with sharp coding instincts as your guideBuild confidence and coding skills with step-by-step explanations that gradually increase your understandingReinforce your learning through mini-projects and exercises at the end of every chapterPurchase of the print or Kindle book includes a free PDF eBookBook DescriptionThis is not your average Python programming book, because the world doesn’t need another one of those. Instead, it’s an illustrated, fun, and hands-on guide that treats learning Python like the adventure it should be. It’s designed especially for beginners who want to understand how code works without getting overwhelmed. You’ll be guided by a cheeky, know-it-all cat who’s surprisingly good at teaching Python from scratch. Don’t worry about going through it alone; a slightly moody dachshund dog is your study buddy, learning right alongside you. Each chapter introduces a core programming concept, explains it with a playful twist, and reinforces it through human-friendly examples, analogies, and exercises. Whether you’re a software professional or someone who’s never written a single line of code, this book will help you build real Python coding skills… and even enjoy the process (shocking, right?). Forget dry tutorials and walls of text. Python Illustrated speaks to visual learners, creative thinkers, cat lovers, dog lovers, and anyone who prefers their learning with a dash of humor. From writing your first function to understanding object-oriented programming, you’ll build a solid foundation in Python (without the usual headaches). What you will learnSet up Python and write your first programUnderstand variables, data types, and conditional statementsUse loops, lists, dictionaries, and tuples to handle data efficientlyWrite and use functions to create reusable codeManage files and understand object-oriented programming and inheritanceDebug your Python code to ensure it works flawlesslyDiscover how you can keep learning and building beyond this bookWho this book is forThis book is ideal for anyone with a sense of humour who’s new to Python or programming in general. It takes a step-by-step hands-on approach that will work for anyone with a practical mindset. Whether you're a student or a professional developer looking to expand your skill set, this book offers a comprehensive and enjoyable learning experience.
R 1,303.00
Interior Point Methods of Mathematical Programming
One has to make everything as simple as possible but, never more simple. Albert Einstein Discovery consists of seeing what every body has seen and thinking what nobody has thought. Albert S. entGyorgy; The primary goal of this book is to provide an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems. The Simplex Method has dominated the theory and practice of mathematical pro gramming since 1947 when Dantzig discovered it. In the fifties and sixties several attempts were made to develop alternative solution methods. At that time the prin cipal base of interior point methods was also developed, for example in the work of Frisch (1955), Caroll (1961), Huard (1967), Fiacco and McCormick (1968) and Dikin (1967). In 1972 Klee and Minty made explicit that in the worst case some variants of the simplex method may require an exponential amount of work to solve Linear Programming (LP) problems. This was at the time when complexity theory became a topic of great interest. People started to classify mathematical programming prob lems as efficiently (in polynomial time) solvable and as difficult (NP-hard) problems. For a while it remained open whether LP was solvable in polynomial time or not. The break-through resolution ofthis problem was obtained by Khachijan (1989).
R 9,006.55
R 344.00
Non-programmers Tutorial for Python
This book is a tutorial for the Python 2 programming language designed for someone with no programming experience. (Note that there are other editions of this book for Python 2.6+ and for Python 3+)
R 422.67
R 580.00
