Mixing
Resources for Learning Hyperreal Numbers
$begingroup$
I've somewhat recently discovered hyperreal numbers, but I haven't gotten the chance to thoroughly research them.
What resources do you all recommend for undergrad level study of the hyperreal number line and hyperreal numbers? The "undergrad" criterion includes resources that cover hyperreals from both an undergrad and postgrad level. Please note that I wish to learn both the infinitesimals and hyperreal infinities (as opposed to Cantor's transfinites, the infinity on the Riemann sphere, and any other types of infinities), so resources only concerning infinitesimal calculus do not suffice.
Thanks.
nonstandard-analysis
asked Jan 1 at 12:03
HarrisonOHarrisonO
414
$endgroup$
add a comment |
$begingroup$
I've somewhat recently discovered hyperreal numbers, but I haven't gotten the chance to thoroughly research them.
What resources do you all recommend for undergrad level study of the hyperreal number line and hyperreal numbers? The "undergrad" criterion includes resources that cover hyperreals from both an undergrad and postgrad level. Please note that I wish to learn both the infinitesimals and hyperreal infinities (as opposed to Cantor's transfinites, the infinity on the Riemann sphere, and any other types of infinities), so resources only concerning infinitesimal calculus do not suffice.
Thanks.
nonstandard-analysis
asked Jan 1 at 12:03
HarrisonOHarrisonO
414
$endgroup$
$begingroup$
The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
$endgroup$
– InequalitiesEverywhere
Jan 1 at 12:20
3
$begingroup$
also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
$endgroup$
– Masacroso
Jan 1 at 12:22
$begingroup$
Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
$endgroup$
– Mark S.
Jan 1 at 14:03
add a comment |
$begingroup$
I've somewhat recently discovered hyperreal numbers, but I haven't gotten the chance to thoroughly research them.
What resources do you all recommend for undergrad level study of the hyperreal number line and hyperreal numbers? The "undergrad" criterion includes resources that cover hyperreals from both an undergrad and postgrad level. Please note that I wish to learn both the infinitesimals and hyperreal infinities (as opposed to Cantor's transfinites, the infinity on the Riemann sphere, and any other types of infinities), so resources only concerning infinitesimal calculus do not suffice.
Thanks.
nonstandard-analysis
asked Jan 1 at 12:03
HarrisonOHarrisonO
414
$endgroup$
I've somewhat recently discovered hyperreal numbers, but I haven't gotten the chance to thoroughly research them.
What resources do you all recommend for undergrad level study of the hyperreal number line and hyperreal numbers? The "undergrad" criterion includes resources that cover hyperreals from both an undergrad and postgrad level. Please note that I wish to learn both the infinitesimals and hyperreal infinities (as opposed to Cantor's transfinites, the infinity on the Riemann sphere, and any other types of infinities), so resources only concerning infinitesimal calculus do not suffice.
Thanks.
nonstandard-analysis
nonstandard-analysis
asked Jan 1 at 12:03
HarrisonOHarrisonO
414
asked Jan 1 at 12:03
HarrisonOHarrisonO
414
asked Jan 1 at 12:03
HarrisonOHarrisonO
414
asked Jan 1 at 12:03
HarrisonOHarrisonO
414
asked Jan 1 at 12:03
HarrisonOHarrisonO
414
414
$begingroup$
The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
$endgroup$
– InequalitiesEverywhere
Jan 1 at 12:20
3
$begingroup$
also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
$endgroup$
– Masacroso
Jan 1 at 12:22
$begingroup$
Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
$endgroup$
– Mark S.
Jan 1 at 14:03
add a comment |
$begingroup$
The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
$endgroup$
– InequalitiesEverywhere
Jan 1 at 12:20
3
$begingroup$
also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
$endgroup$
– Masacroso
Jan 1 at 12:22
$begingroup$
Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
$endgroup$
– Mark S.
Jan 1 at 14:03
$begingroup$
The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
$endgroup$
– InequalitiesEverywhere
Jan 1 at 12:20
$begingroup$
The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
$endgroup$
– InequalitiesEverywhere
Jan 1 at 12:20
3
3
$begingroup$
also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
$endgroup$
– Masacroso
Jan 1 at 12:22
$begingroup$
also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
$endgroup$
– Masacroso
Jan 1 at 12:22
$begingroup$
Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
$endgroup$
– Mark S.
Jan 1 at 14:03
$begingroup$
Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
$endgroup$
– Mark S.
Jan 1 at 14:03
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3058431%2fresources-for-learning-hyperreal-numbers%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3058431%2fresources-for-learning-hyperreal-numbers%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
The place where it all began is ostensibly Robinson's Non-standard Analysis. That might be where you want to start as well.
$endgroup$
– InequalitiesEverywhere
Jan 1 at 12:20
3
$begingroup$
also consider the textbook Lectures on the Hyperreals: An Introduction to Nonstandard Analysis of Robert Goldblatt. I didnt read it.
$endgroup$
– Masacroso
Jan 1 at 12:22
$begingroup$
Keisler's "Elementary Calculus" is not fully rigorous, but gives some intuition at a basic level about the applications of Robinson's hyperreals to Calculus. It doesn't "only concern infinitesimal calculus" since you need infinities for things like integrals, etc.
$endgroup$
– Mark S.
Jan 1 at 14:03