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While taking a course on introductory probability, I found out about stochastic calculus and differential equations, topics which I decided I would learn because they sounded very interesting. I found an MIT OCW course on Mathematical Finance that was perfect because it would use single and multivariable calculus, differential equations, linear algebra and probability, as well as develop the concepts of Itô Calculus and Stochastic processes.
Unfortunately, the course problems had no solutions (a problem I find very hindering when learning on my own because an integral part of the learning process is known when you are right, when you are not, and why you are not). Also, the lecture notes contained typos who managed to invade equations and formulas, making them false and confusing.
I have looked for similar courses on the internet that both reinforce and review topics I have already studied while also developing the aforementioned concepts that I wished to understand, however, my search has turned up nothing.
I would like to know if there are books or online courses with these characteristics, or at least a website or textbook I can use to learn stochastic calculus.

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The following textbook may be a good fit:

Steven Roman

Introduction to the Mathematics of Finance

Springer, 2004

It has lots of worked examples, and has an appendix with solutions to selected exercises (most of the odd-numbered ones).

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  • $\begingroup$ This book seems great. I checked some previews and it seems to contain stochastic processes, martingales and filtrations, as well as Itô's lemma, which are all topics I wanted to study, but the preview only showed a few mentions of SDE's. Does the book cover this topic? $\endgroup$ – Guacho Perez Dec 29 '16 at 1:30
  • $\begingroup$ @Guacho Perez: Roman's text, while rigorous, is an undergraduate text. It brushes up against SDE, but stops just short of trying to develop that theory. For the most part, SDE is a graduate level topic. $\endgroup$ – quasi Mar 25 '17 at 20:22
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Consider Kellison's Theory of Interest. There's solutions for every problem on his website, and the book itself is decent.

It might be more novice than what you have in mind, but if you're starting out, it's good enough.

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  • $\begingroup$ I looked at it but it seemed to be more economically rather than mathematically oriented. $\endgroup$ – Guacho Perez Dec 29 '16 at 1:25
  • $\begingroup$ Try the later chapters. Believe me, the book is vigorous - there's extensive summations and fine details on most financial instruments. It starts off from baby basics, but they do get into stochastic processes at the end. $\endgroup$ – Ryan Dec 30 '16 at 1:49

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