Our book is titled Recent Advances in Mathematics. The book primarily discusses the new methodologies, including statistical analysis, theoretical analysis, modified method analysis, and comparisons between the new and traditional methodologies. Each chapter has certain techniques for summing up the issues that clarify the ideas. Each topic is presented with care and it is hoped that the book will satisfy the needs of scholars from various professional fields. For their particular interests, the research in this field is therefore very significant and helpful. I’d like to thank the authors for their invaluable works and also the publishing house for their cooperation.