This textbook is a revised version based on Mathematics (2nd Edition), a pre-college textbook for foreign students studying in China. The revision refers to the Pre-University Education Standards for Foreigners Studying in China (Trial Version) and incorporates the teaching experience gained from instructing international students in recent years.

The textbook is divided into 5 parts: Algebra, Plane Analytic Geometry, Spatial Analytic Geometry, Limits and Derivatives of Functions, and Probability and Statistics, covering a total of 20 chapters. It includes most of the senior high school mathematics knowledge required for advanced mathematics, such as sets, inequalities, functions, trigonometric functions, sequences, and plane vectors. Meanwhile, in order to better bridge senior high school mathematics and university mathematics, the textbook appropriately extends to university-level mathematics content, adding topics like spatial vectors, spatial planes and spatial lines, limits of sequences and functions, and applications of derivatives.

Ren Weiyun, PhD in Science, is an Associate Professor at the School of Mathematics, Tianjin University. Her research mainly focus on functional analysis. Professor Ren has published 14 papers in important academic journals at home and abroad, and participated in 4 National Natural Science Foundation projects and 4 educational reform projects of Tianjin University. Since 2007, she has been engaged in the teaching and test proposition of pre-college mathematics, and took part in the formulation of Pre-University Mathematics Teaching Syllabus and Pre-University Education Standards for Foreigners Studying in China (Trial Version).

Guo Fei, PhD of Nankai University, is a Professor at the School of Mathematics, Tianjin University. Professor Guo has presided over and participated in 3 National Natural Science Foundation projects, and published more than 20 papers in SCI-indexed journals. Dedicated to front-line teaching, she has been engaged in the teaching of university public mathematics courses for 20 years. She serves as the chief editor of 5 textbooks and teaching aids, including Mathematics and Mathematics Handbook, special textbooks for Chinese Government Scholarship recipients. Professor Guo has also presided over and participated in 17 educational reform projects at Tianjin and university levels, and won multiple awards such as the Second Prize of Tianjin Teaching Achievements, the Second Prize of Tianjin Young Teachers’ Basic Skills Competition, and the title of “Excellent Instructor” in the National and Tianjin University Students Mathematics Competitions five times.

◎ Aligns with the Pre-University Education Standards for Foreigners Studying in China (Trial Version)

◎ Connects content with undergraduate major studies

◎ Emphasizes application and provides follow-up exercises

◎ Uses simple language that is easy to understand

This textbook can be used not only as a mathematics textbook for foreign pre-college students studying in China, but also as a reference book for first-year undergraduate students in domestic universities to learn advanced mathematics.

This textbook emphasizes the application of theorems and formulas. Examples are provided immediately after the conclusions, and a large number of after-class exercises are included for learners to practice. At the end of the book, mathematical terms in the textbook are listed in chapter order, and a Chinese-English Table of Mathematical Symbols is also provided for learners’ reference.