Conversations for the Mathematics Community

Hello,

My name is Craig.  I was referred to MAA Connect by MAA member services.  Although none of the MAA Connect communities seemed the perfect fit for my concerns, I thought this community seemed like the closest.  I hope it is OK for me to post here.

I am not a mathematician.  I started my college career by studying engineering, but then changed to computer science and earned a bachelors degree.  Nevertheless, while studying engineering, I had a lot of mathematics courses such as calculus, differential equations, and statistics. But, that was upwards of thirty years ago, so some refreshing is definitely needed to pick this material up again.

Truthfully, I have had some regrets in later years that I didn't major in mathematics instead.  I am disabled, so I no longer practice computer programming for a vocation.

I would very much like to learn how to do mathematical proofs and eventually work through material in abstract algebra, topology, differential geometry, and real analysis.  In the past I have taken the initiative to work partly through a "bridges to higher level mathematics" book, but got bogged down when the proofs became more involved and provided solutions more sparse.  I understand that as one progresses in higher level, proof based mathematics, increasing material is left out of proofs since certainly things are assumed by way of expert experience with the subject matter.  I understand the benefit of being involved in a math program is to master these stylistic concerns.

However, I am interested in networking for resources for lay people to receive tutoring from others to learn proof based mathematics.  I don't know if there are math students or others out there that could benefit from tutoring lay people like myself on a pro bono basis?

-- Craig

------------------------------
Craig Ugoretz
Plymouth WI
------------------------------

Hi Craig. I have a very similar story. I'm an adult who completed the calculus sequence, Differential Equations, Linear Algebra many years ago. Due to health issues and disability, I never completed my math degree but have a strong interest in studying higher level math now. Perhaps we can work together through some online materials (MIT opencourseware or HW sets from other universities) as partners, as we are in a similar boat. We could at very least keep each other inspired? I'm sure there are also math tutors who might be willing to help with proof writing and proof based courses?

------------------------------
Erica Milam
Disability
Oakland CA
------------------------------

Original Message:
Sent: 01-07-2021 17:28
From: Craig Ugoretz
Subject: Lay learning of proof based mathematics

Hello,

My name is Craig.  I was referred to MAA Connect by MAA member services.  Although none of the MAA Connect communities seemed the perfect fit for my concerns, I thought this community seemed like the closest.  I hope it is OK for me to post here.

I am not a mathematician.  I started my college career by studying engineering, but then changed to computer science and earned a bachelors degree.  Nevertheless, while studying engineering, I had a lot of mathematics courses such as calculus, differential equations, and statistics. But, that was upwards of thirty years ago, so some refreshing is definitely needed to pick this material up again.

Truthfully, I have had some regrets in later years that I didn't major in mathematics instead.  I am disabled, so I no longer practice computer programming for a vocation.

I would very much like to learn how to do mathematical proofs and eventually work through material in abstract algebra, topology, differential geometry, and real analysis.  In the past I have taken the initiative to work partly through a "bridges to higher level mathematics" book, but got bogged down when the proofs became more involved and provided solutions more sparse.  I understand that as one progresses in higher level, proof based mathematics, increasing material is left out of proofs since certainly things are assumed by way of expert experience with the subject matter.  I understand the benefit of being involved in a math program is to master these stylistic concerns.

However, I am interested in networking for resources for lay people to receive tutoring from others to learn proof based mathematics.  I don't know if there are math students or others out there that could benefit from tutoring lay people like myself on a pro bono basis?

-- Craig

------------------------------
Craig Ugoretz
Plymouth WI
------------------------------

Hello Erica and Craig,

I have a math degree (doctorate, Univ of KY, 2004) but for the last 10 years have spent much time tutoring adults in mathematics at various levels. I would be willing to be a (pro bono) resource for you and Craig in terms of learning proof writing or working through an online course like the (MIT opencourseware or something similar...something free and open preferred). Or we could choose a not-too-expensive book and work through parts of it (there are lots of not-too-expensive options such as old editions, used copies, and so-forth).

I've tried to work through a couple of chapters of various books over the last few years just to learn some areas of math that I did not specialize in, or to remind myself of things I don't use often. (For example, the last thing I worked on was "An Illustrated Theory of Numbers" by Martin Weissman because I wanted to learn more number theory, but I did not finish all the chapters I planned to.) I'm willing to look at any level -- calculus, introduction to proofs, on up to graduate level material. So I'd enjoy working through some organized material and talking with other people about it. Perhaps my formal training can be a benefit if things get sticky but more important, I think, is the effort of everyone to help each other learn. I always learn something new even if it's a topic I think I already "know"...and there's plenty of stuff I know I don't know.

Depending on your interest and available time to commit, maybe we could zoom with each other to go over problem sets or talk about what we've read. Or we can just do it over email or chat somewhere.  Perhaps once a month? Every 2 weeks? More often? I suppose life can get in the way but sometimes just a regular schedule can keep something moving forward.

Let me know what you think.

Leigh

------------------------------
Leigh Noble
mathematics coach and computer systems administrator
Self-Employed -- Contractor With Simiode.Org
Winnipeg MB
------------------------------

Original Message:
Sent: 01-08-2021 12:49
From: Erica Milam
Subject: Lay learning of proof based mathematics

Hi Craig. I have a very similar story. I'm an adult who completed the calculus sequence, Differential Equations, Linear Algebra many years ago. Due to health issues and disability, I never completed my math degree but have a strong interest in studying higher level math now. Perhaps we can work together through some online materials (MIT opencourseware or HW sets from other universities) as partners, as we are in a similar boat. We could at very least keep each other inspired? I'm sure there are also math tutors who might be willing to help with proof writing and proof based courses?

------------------------------
Erica Milam
Disability
Oakland CA

Original Message:
Sent: 01-07-2021 17:28
From: Craig Ugoretz
Subject: Lay learning of proof based mathematics

Hello,

My name is Craig.  I was referred to MAA Connect by MAA member services.  Although none of the MAA Connect communities seemed the perfect fit for my concerns, I thought this community seemed like the closest.  I hope it is OK for me to post here.

I am not a mathematician.  I started my college career by studying engineering, but then changed to computer science and earned a bachelors degree.  Nevertheless, while studying engineering, I had a lot of mathematics courses such as calculus, differential equations, and statistics. But, that was upwards of thirty years ago, so some refreshing is definitely needed to pick this material up again.

Truthfully, I have had some regrets in later years that I didn't major in mathematics instead.  I am disabled, so I no longer practice computer programming for a vocation.

I would very much like to learn how to do mathematical proofs and eventually work through material in abstract algebra, topology, differential geometry, and real analysis.  In the past I have taken the initiative to work partly through a "bridges to higher level mathematics" book, but got bogged down when the proofs became more involved and provided solutions more sparse.  I understand that as one progresses in higher level, proof based mathematics, increasing material is left out of proofs since certainly things are assumed by way of expert experience with the subject matter.  I understand the benefit of being involved in a math program is to master these stylistic concerns.

However, I am interested in networking for resources for lay people to receive tutoring from others to learn proof based mathematics.  I don't know if there are math students or others out there that could benefit from tutoring lay people like myself on a pro bono basis?

-- Craig

------------------------------
Craig Ugoretz
Plymouth WI
------------------------------

Craig:

If you look at the Pareto effect of important data, in every case 80 percent of the relevant data resides in 20% of the materials.
My point of view is the review the 20% of the most relevant data first in class and with that data the proofs come naturally, as it is used every day.
Everyone in the field can assist you with understanding the proof applications of the data that is a small percentage of the whole, but widely used.
The other 80% should only use proofs it it is of interest to the student, but the 80% of the most critical mathematical information in any math book is held in 20% of the materials.  In all classes that 20%should be taught first and considered a priority.  Just think how much easier math would be if you had the option to focus on the remaining 80% after learning just 20% of the most relevant proofs  Tomasmcnellis@gmail.com




5

------------------------------
Thomas McNellis
President
Memory Matters Corporation
West Chester PA
------------------------------

Original Message:
Sent: 01-07-2021 17:28
From: Craig Ugoretz
Subject: Lay learning of proof based mathematics

Hello,

My name is Craig.  I was referred to MAA Connect by MAA member services.  Although none of the MAA Connect communities seemed the perfect fit for my concerns, I thought this community seemed like the closest.  I hope it is OK for me to post here.

I am not a mathematician.  I started my college career by studying engineering, but then changed to computer science and earned a bachelors degree.  Nevertheless, while studying engineering, I had a lot of mathematics courses such as calculus, differential equations, and statistics. But, that was upwards of thirty years ago, so some refreshing is definitely needed to pick this material up again.

Truthfully, I have had some regrets in later years that I didn't major in mathematics instead.  I am disabled, so I no longer practice computer programming for a vocation.

I would very much like to learn how to do mathematical proofs and eventually work through material in abstract algebra, topology, differential geometry, and real analysis.  In the past I have taken the initiative to work partly through a "bridges to higher level mathematics" book, but got bogged down when the proofs became more involved and provided solutions more sparse.  I understand that as one progresses in higher level, proof based mathematics, increasing material is left out of proofs since certainly things are assumed by way of expert experience with the subject matter.  I understand the benefit of being involved in a math program is to master these stylistic concerns.

However, I am interested in networking for resources for lay people to receive tutoring from others to learn proof based mathematics.  I don't know if there are math students or others out there that could benefit from tutoring lay people like myself on a pro bono basis?

-- Craig

------------------------------
Craig Ugoretz
Plymouth WI
------------------------------

Hi, Craig,

A couple of words, both as someone who teaches a proof writing bridge course and as a mathematician who has attempted to learn new areas independently.

First, my (now retired) colleague Ted Sundstrom has a a book that I use that is a nice introduction to different techniques used in writing proofs, and it's available for free as a PDF: Mathematical Reasoning: Writing and Proof, https://www.tedsundstrom.com/mathematical-reasoning-writing-and-proof

You don't mention the nature of your disability, so if the PDF isn't accessible for you (a real issue with a lot of mathematical content) let me know and we can discuss alternative formats.

Second, it's a little discussed fact that proofs are quite often (I would say most often) not written to invite the reader on the journey of discovery. The nature of mathematical investigation is often very different from mathematical justification. This often leads to frustration for the reader who is new to the material. This is true at the beginning proof level and at the research level if you are trying to learn a new area.

The web comic Abstruse Goose gets pretty close to the real proof process, https://abstrusegoose.com/230. In case you don't want to or can't read the comic, the gist is that developing a proof is like driving around lost, looking for some destination in an unfamiliar place (with your GPS not working), while the proof is written as turn-by-turn directions as if you knew where you were going all along.

My point is that the proof itself is almost always the very last thing that is done and all the work leading up to the proof is where the real value is. Too often, that work is only hinted at and left for the reader to rediscover. So, if you find yourself frustrated, be aware that the frustration may not be with you grasp of the concepts, but with the presentation. I think by far the most common reaction of students to reading an involved proof is "I see why that works, but I have no idea how they came up with it."

Finally, as others have offered, I am happy to answer questions you have along your journey via email.

------------------------------
Clark Wells
Associate Professor
Pronouns: he/him/his
Grand Valley State University
Allendale MI 49401
office: 616-331-2444
wellsc@gvsu.edu
------------------------------

Original Message:
Sent: 01-07-2021 17:28
From: Craig Ugoretz
Subject: Lay learning of proof based mathematics

Hello,

My name is Craig.  I was referred to MAA Connect by MAA member services.  Although none of the MAA Connect communities seemed the perfect fit for my concerns, I thought this community seemed like the closest.  I hope it is OK for me to post here.

I am not a mathematician.  I started my college career by studying engineering, but then changed to computer science and earned a bachelors degree.  Nevertheless, while studying engineering, I had a lot of mathematics courses such as calculus, differential equations, and statistics. But, that was upwards of thirty years ago, so some refreshing is definitely needed to pick this material up again.

Truthfully, I have had some regrets in later years that I didn't major in mathematics instead.  I am disabled, so I no longer practice computer programming for a vocation.

I would very much like to learn how to do mathematical proofs and eventually work through material in abstract algebra, topology, differential geometry, and real analysis.  In the past I have taken the initiative to work partly through a "bridges to higher level mathematics" book, but got bogged down when the proofs became more involved and provided solutions more sparse.  I understand that as one progresses in higher level, proof based mathematics, increasing material is left out of proofs since certainly things are assumed by way of expert experience with the subject matter.  I understand the benefit of being involved in a math program is to master these stylistic concerns.

However, I am interested in networking for resources for lay people to receive tutoring from others to learn proof based mathematics.  I don't know if there are math students or others out there that could benefit from tutoring lay people like myself on a pro bono basis?

-- Craig

------------------------------
Craig Ugoretz
Plymouth WI
------------------------------