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A structural approach to abstract algebra, providing a transparent and mathematically sound introduction to groups, rings, and fields.
The text is built on the philosophy that abstraction should never be divorced from algorithmic computation; every abstract definition is paired with a computational constraint or a highly verifiable example to ensure deep intuition. The first semester focuses on Group Theory, culminating in the Isomorphism Theorems, while the second semester develops the factorization properties of integral domains and Field Theory. The text concludes with a comprehensive treatment of Galois Theory, where students experience the climax of the undergraduate sequence, observing the synthesis of group and field theory as subgroups perfectly mirror intermediate extensions.
Paul L. Dayao is a faculty member at the Ateneo de Manila University with over a decade of teaching experience to his writing. His research interests lie in Real Analysis and Functional Analysis. He has recently published works on integration theory in the Missouri Journal of Mathematical Sciences (MJMS) and Real Analysis Exchange (RAEx).
In addition to his research, he is an active textbook author. He has another manuscript currently under consideration at major publishers: Fundamentals of Classical Banach Space Theory (under review at CRC) and Linear Algebra: A Coordinate-Free Approach (being considered for publication by Springer). He is also finalizing his PhD application in Measure Theory at the University of St Andrews. As a dedicated educator, he specializes in creating “teaching-led” mathematical materials that bridge the gap between intuition and rigor.