Solutions to Selected Exercises

These notes contain hints and (sometimes) solutions to the exercises in the book From Calculus to Cohomology by I. Madsen and J. Tornehave. Some portions of the notes may contain some details added to the theory part of the book. I will keep updating the notes attached here.  For some of the answers, I had to look at different web-based discussions and resources. Please write me an email if you find errors in the solutions or any typographical mistakes.

These notes contain hints and (sometimes) solutions to the exercises in the book Real Analysis by H. Royden and P. Fitzpatrick. Some portions of the notes may contain some details added to the theory part of the book. I will keep updating the notes attached here.  For some of the answers, I had to look at different web-based discussions and resources. Please write me an email if you find errors in the solutions or any typographical mistakes.

In Section 2.7, I have given a detailed and rigorous account of the Cantor set and the Cantor function. This could be pretty useful to beginners. Also, in the exercises of Section 3.1, I have discussed the properties of the Borel measurable functions in detail, which is another theoretical highlight of the material.

These notes contain hints and (sometimes) solutions to the exercises from Sections 51-82 in the book Topology by J. Munkres and exercises from the book Algebraic Topology by A. Hatcher. Some portions of the notes may contain some details added to the theory part of the book. I also plan to add any relevant exercises from the previous section at some later point of time. I will keep updating the notes attached here.  For some of the answers, I had to look at different web-based discussions and resources. Please write me an email if you find errors in the solutions or any typographical mistakes. Later I plan to add solutions to exercises from the book Elements of Algebraic Topology by J. Munkres in the third part of this note.