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Good point! That said, disclosing the result in the question could be to make the question more doable / less intimidating for the student, so they know what to aim for. Note that popular undergraduat …

One option is Engineering Mathematics: A Foundation for Electronic, Electrical, Communications, and Systems Engineers by Croft et al. I have taught using this for several years. It is replete with ele …

Preamble: In my experience, many introductory engineering mathematics textbooks these days tend to skip proofs and discuss logic only in the context of digital electronics. … I hasten to add that many engineering mathematics textbooks do have strong points, such as numerous examples of mathematics applied to solving engineering problems. …

The answer by user1149748 is very good and covers several important points. I'd like to add a few further thoughts. Other things to consider include what is your starting point and what do you assume …

When writing a textbook, the key is to know your audience and make it clear who that audience is, including expected background and aims. State it in the preface and, if you have any control over what …

An alternative approach is Childs' A Concrete Introduction to Higher Algebra (3rd ed., Springer 2008). It starts with some basic number theory, followed by rings and fields. Groups don't make an appea …

Following up on Mike Miller's comment that "many incredible textbooks have incredible exercises," you might want to take a look at Pugh's Real Mathematical Analysis for its excellent selection of problems …

Caveat: this answer is predicated on the student having "a fairly good grip of some abstract algebra and real analysis [and] who wants to gain a rigorous and precise knowledge of the topic [of linear …

Worth a mention is Pons' Real Analysis for the Undergraduate: With an Invitation to Functional Analysis. While it is primarily an introductory real analysis text, the final section of each chapter is …

Calculus Problems by Baronti, De Mari, van der Putten & Venturi might be worth a look. It has problems on all the topics you mention, along with basic ordinary differential equations. There is also a …

An unusual choice could be Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra by Cox, Little and O'Shea. It may not necessarily be a popular …

Judson's Abstract Algebra: Theory and Applications is different in that it is an open source textbook that is available at no cost. I haven't used it (yet), but I think it's worth pointing out for the …

I think this is only a partial answer to your question. Ideals, Varieties, and Algorithms by Cox, Little & O'Shea presents affine varieties and their parametrizations in Sections 2 and 3, respectively …

You do not mention differential equations, but this is a very useful topic in engineering, aerospace included, and the list of topics/courses you have studied mean that you would be well prepared for …

Thanks in part to Jyrki Lahtonen's remarks on coding theory and cryptography, I have an applied algebra book to suggest: Algebra for Applications, Arkadii Slinko, 2nd ed., 2020 Springer The preface to …