This is the final draft of my write-up for this course, with the only changes made from the previous being minor revisions and edits.
Salvador_Balkus___MTH311_Final_Paper (1)
Final Report Draft
I have taken all of my posts this semester and compiled them into a draft of a final report. Enjoy!
Salvador_Balkus___MTH311_Final_PaperWeek 13 – Computability
This week, I added a short proof regarding computability to my previous work on real numbers.
Week_13___ComputabilityWeek 12 – Dedekind Cuts
This week we defined the set of real numbers more formally by discussing Dedekind cuts. I demonstrated some proofs of properties of the real numbers, including addition, multiplication, ordering, and completeness. Week_12___One_Way_to_Construct_the_Real_Numbers
Week 11 – Sequences of Functions
This week I researched pointwise and uniform convergence but got stuck trying to prove convergence of the Taylor Series for sin(x).
Week_11___Sequences_of_FunctionsWeek 10 – Cauchy Sequences
This week I continued with proofs related to Cauchy sequences, specifically relating the sequence to series convergence and proving that a sequence is not a Cauchy sequence.
Week_10___Cauchy_Sequences_and_Real_Numbers (1)
Week 9 – Cauchy Sequences
Professor Davis presented an interesting and, to my understanding, somewhat unorthodox way of constructing the real numbers using a mathematical idea called a Cauchy Sequence. This week, I worked on proofs involving these Cauchy sequences.
Week_9___Cauchy_Sequences_and_Real_Numbers
Week 8 – Limits
This week we took another detour before getting to the construction of the real numbers to discuss limits.
Week_8___LimitsWeek 7 & 1/2
Just a quick update to correct an error in a proof from last week.
Week_7___Continuous_Functions_on_the_Rationals (1)Week 7
This week we took a slight detour before getting to the real numbers to discuss proving the continuity of rational-valued functions using delta-epsilon arguments.
Week_7___Continuous_Functions_on_the_Rationals