# Auxiliary Material- Mathematics for Computer and Information Sciences

*2024-07-15*

# Preface

Welcome to a transformative journey through the mathematical foundations essential for modern computer and information science. This auxiliary material is tailored for B.Tech. Computer Science students as part of the 2024 curriculum introduced by APJAKTU, which is at the forefront of revolutionizing engineering education in Kerala to meet international standards. APJAKTU’s initiatives are designed to align its programs with global benchmarks, ensuring our graduates are well-equipped for the demands of the global job market.

Our curriculum progressively covers a range of fundamental topics: Calculus, Linear Algebra, Probability, Statistics, Stochastic Models, and Graph Theory. Each course builds on applied and computational mathematics, providing a cohesive and comprehensive understanding of these critical areas. These subjects are meticulously aligned with practical applications in computer and information science, equipping students with the necessary skills for industrial training and internships.

Throughout the book, we integrate *Python* programming to offer a dynamic learning experience. This approach not only enhances technical proficiency but also deepens understanding of the mathematical principles that drive innovation in computer science. As you progress through this material, tackling concepts from Calculus to Graph Theory with a focus on representation and analysis, this book will serve as a valuable resource, preparing you to excel in both academic and professional arenas, and to meet the highest standards of engineering excellence.

## Why read this book

In the ever-evolving field of computer science, mathematical and logical thinking are critical skills that form the backbone of effective problem-solving and innovative algorithm design. This book, tailored for B.Tech. Computer Science students under the 2024 APJAKTU curriculum, bridges the gap between theoretical mathematics and practical applications in computer and information science. By exploring essential mathematical concepts with real-world examples and interactive demonstrations, students will gain a deep understanding of topics such as algorithm design, probabilistic machine learning, and real-time modelling. This foundation not only enhances their technical proficiency but also equips them with the analytical tools necessary to tackle complex challenges in their professional careers.

## Structure of the book

All four courses in Mathematics for Computer and Information Science are included in this digital material as continues chapters in progressive the order as shown in the APJKTU B.Tech. curriculum 2024.

Chapters 4.1 introduces a new topic, and …

## Software information and conventions

We used the **knitr** package (Xie 2015) and the **bookdown** package (Xie 2024) to compile this material. The R session information is shown below:

```
## R version 4.2.1 (2022-06-23 ucrt)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 22631)
##
## Locale:
## LC_COLLATE=English_India.utf8
## LC_CTYPE=English_India.utf8
## LC_MONETARY=English_India.utf8
## LC_NUMERIC=C
## LC_TIME=English_India.utf8
##
## Package version:
## base64enc_0.1.3 bookdown_0.39.2
## bslib_0.7.0 cachem_1.0.8
## cli_3.6.1 compiler_4.2.1
## digest_0.6.30 evaluate_0.24.0
## fastmap_1.1.1 fontawesome_0.5.2
## fs_1.6.3 glue_1.6.2
## graphics_4.2.1 grDevices_4.2.1
## grid_4.2.1 here_1.0.1
## highr_0.11 htmltools_0.5.8.1
## jquerylib_0.1.4 jsonlite_1.8.8
## knitr_1.46.3 lattice_0.20-45
## lifecycle_1.0.4 magrittr_2.0.3
## Matrix_1.6-1 memoise_2.0.1
## methods_4.2.1 mime_0.12
## png_0.1-8 R6_2.5.1
## rappdirs_0.3.3 Rcpp_1.0.11
## RcppTOML_0.2.2 reticulate_1.36.0
## rlang_1.1.1 rmarkdown_2.24
## rprojroot_2.0.3 rstudioapi_0.15.0
## sass_0.4.9 stats_4.2.1
## stringi_1.7.12 stringr_1.5.0
## tinytex_0.51.1 tools_4.2.1
## utils_4.2.1 vctrs_0.6.3
## withr_2.5.0 xfun_0.43
## yaml_2.3.8
```

## Acknowledgments

This auxiliary material is the result of collaborative efforts and forward-thinking initiatives spearheaded by the higher officials of APJKTU, along with the chairmen, conveners, and members of various Boards of Studies. The idea of creating supplementary resources to support both students and faculty members in the learning and teaching process was proposed by these dedicated individuals. Their vision and commitment to excellence in engineering education have been instrumental in shaping these materials.

We extend our heartfelt gratitude to the students, whose feedback has been the main pillar behind this initiative. Their insights and experiences have guided us in crafting content that meets their needs and exceeds their expectations. This auxiliary material aims to enhance their academic journey and prepare them for successful careers in computer and information science.

Board of Studies

Computer Science & Allied courses### References

*Dynamic Documents with R and Knitr*. 2nd ed. Boca Raton, Florida: Chapman; Hall/CRC. http://yihui.name/knitr/.

*Bookdown: Authoring Books and Technical Documents with r Markdown*. https://github.com/rstudio/bookdown.