Mathematics and Statistics for Science

Mathematics and statistics are the bedrock of modern science. No matter which branch of science you plan to work in, you simply cannot avoid quantitative approaches. And while you won’t always need to know a great deal of theory, you will need to know how to apply mathematical and statistical methods in realistic scenarios. That is precisely what this book teaches. It covers the mathematical and statistical topics that are ubiquitous in early undergraduate courses, but does so in a way that is directly linked to science.
Beginning with the use of units and functions, this book covers key topics such as complex numbers, vectors and matrices, differentiation (both single and multivariable), integration, elementary differential equations, probability, random variables, inference and linear regression. Each topic is illustrated with widely-used scientific equations (such as the ideal gas law or the Nernst equation) and real scientific data, often taken directly from recent scientific papers. The emphasis throughout is on practical solutions, including the use of computational tools (such as Wolfram Alpha or R), not theoretical development. There is a large number of exercises, divided into mathematical drills and scientific applications, and full solutions to all the exercises are available to instructors.
Mathematics and Statistics for Science covers the core methods in mathematics and statistics necessary for a university degree in science, highlighting practical solutions and scientific applications. Its pragmatic approach is ideal for students who need to apply mathematics and statistics in a real scientific setting, whether in the physical sciences, life sciences or medicine.

數學和統計是現代科學的基石。無論你計劃在科學的哪個領域工作，你都無法避免使用定量方法。雖然你不總是需要了解大量的理論，但你需要知道如何在實際情境中應用數學和統計方法。這本書正是教授這一點的。它涵蓋了在大學早期課程中無處不在的數學和統計主題，但以與科學直接相關的方式進行介紹。

從單位和函數的使用開始，這本書涵蓋了關鍵主題，如複數、向量和矩陣、微分（單變量和多變量）、積分、初等微分方程、概率、隨機變量、推論和線性回歸。每個主題都以廣泛使用的科學方程式（如理想氣體定律或涅爾斯特方程式）和真實科學數據為例，這些數據通常直接來自最近的科學論文。整本書的重點都放在實際解決方案上，包括使用計算工具（如Wolfram Alpha或R），而不是理論發展。書中有大量的練習題，分為數學練習和科學應用，並且所有練習的完整解答都提供給教師使用。

《數學和統計學為科學服務》涵蓋了科學學位所需的數學和統計核心方法，強調實際解決方案和科學應用。它的實用方法非常適合需要在真實科學環境中應用數學和統計的學生，無論是在物理科學、生命科學還是醫學領域。

​James Sneyd is a Professor of Applied Mathematics at the University of Auckland, New Zealand. His research is mostly in mathematical physiology and cell biology, and he is the co-author (with Jim Keener) of the prize-winning book Mathematical Physiology. He lives beside a beach, and it is absolutely untrue that he would ever waste his time playing computer games.
Rachel Fewster is a Professor of Statistics at the University of Auckland, New Zealand. She has over 20 years experience of teaching mathematical statistics to students with diverse interests, for which she has received a national tertiary educator award. She is a leading researcher in statistical methods for wildlife conservation, and has pioneered numerous methods for analysing novel data types generated by emerging technologies for remote sensing and animal recognition. She leads a large citizen science project for New Zealand community conservationists and enjoys the challenge of communicating technical information to diverse audiences in an engaging and accessible manner. She is a recipient of the Campbell Award, the premier award for New Zealand statisticians.
Duncan McGillivray is a Professor of Physical Chemistry at the University of Auckland, New Zealand, and a Fellow of the Royal Society of Chemistry and the New Zealand Institute of Chemistry. He uses a wide range of mathematical tools in his studies of biologically relevant colloids and interfaces using neutron scattering. He is passionate about teaching and learning for science students, and has been involved in teaching at all levels of tertiary study.

James Sneyd是紐西蘭奧克蘭大學應用數學教授。他的研究主要集中在數學生理學和細胞生物學領域，並與Jim Keener合著了獲獎書籍《數學生理學》。他住在海灘旁，絕對不會浪費時間玩電腦遊戲。

Rachel Fewster是紐西蘭奧克蘭大學統計學教授。她擁有超過20年的教授數學統計學經驗，並因此獲得了國家高等教育獎。她是野生動物保護統計方法的領先研究者，並開創了許多分析新興技術生成的遙感和動物識別數據類型的方法。她領導著一個大型的紐西蘭社區保育公民科學項目，並喜歡以引人入勝和易於理解的方式向不同的觀眾傳達技術信息。她是紐西蘭統計學家的最高獎項Campbell Award的獲得者。

Duncan McGillivray是紐西蘭奧克蘭大學物理化學教授，也是英國皇家化學學會和紐西蘭化學學會的會士。他在生物相關膠體和界面的研究中使用了各種數學工具，並利用中子散射技術進行研究。他對科學學生的教學和學習充滿熱情，並參與了各個學術階段的教學工作。