Thank you again John for taking the time again and again to respond - totally appreciated, it's amazing.

As a consequence, I took the entire day to try your solution, google frantically, but I failed miserably.
I will spare you the details of everything I tried, but here is what i think is my best attempt:

.1.  
Read carefully: https://bookdown.org/yihui/rmarkdown/template-pandoc.html

.2. 
Download default.latex from your website: https://github.com/jgm/pandoc-templates

.3. 
Rename the file to my-template.tex and, as per your email, line 460 just before $body$, add:
$if(dayone)$
\mode<presentation>
   {
     \title[\CourseName{} Lecture $lecture-number$]{\CourseName{} \newline \, Lecture $lecture-number$}
     \date{\DayOne{}\Yr{}}
   }
   ###
   \titlepage
$endif$

.4. 
In my bookdown,  add the $dayone$ custom Pandoc variable
# Notations {#notations}
## Mathematics
$dayone$
```{r Lecture1Outline, eval = (out_type=="beamer"), echo=FALSE, results='asis'}
```
```{r Lecture1Slide1, eval = (out_type=="beamer"), echo=FALSE, results='asis'}
```
`r if (out_type=="beamer") "- "` $h = \left(h_{1}, h_{2}, \ldots, h_{n}\right)$ denotes a vector (lowercase)

etc. etc...

.5.
add "template: my-template.tex" to my YAML so that "--template my-template.tex" is being correctly added as an option to Pandoc.

OUTCOME:

I still get the undesired slide...
"...
Mathematics
𝑑𝑎𝑦𝑜𝑛𝑒
..."

I check the .rmd file.
It has 
<!--chapter:end:index.Rmd-->
# Notations {#notations}
## Mathematics
$dayone$
etc. etc...

the .tex file has:

\hypertarget{mathematics}{%
\subsection{Mathematics}\label{mathematics}}
\begin{frame}{Mathematics}
\(dayone\)
\end{frame}

I am so sorry - I feel crummy I could not figure this one out after so many hours and I Thank you in advance for any further help on this issue that has drawn me for nearly 18 months.
Many thanks
thomas

PS: note that I have 
before_body: beamer_prefix.tex
and that works well for setting the initial cover page (syllabus) - the issue is really after, as I used this mode<presentation> to redefine the elements of the title slide on the fly (day 1, 2, etc of the course)

On Tuesday, August 25, 2020 at 12:22:26 PM UTC+8 John MacFarlane wrote:

If that's what you need, then a custom template could provide it.
Just add this stuff to a custom template, with variables in the
varying parts:

\mode<presentation>
{
\title[\CourseName{} Lecture $lecture-number$]{\CourseName{} \newline \, Lecture $lecture-number$}
\date{\DayOne{}\Yr{}}
}
###
\titlepage

$body$

"Chevrier, Thomas" <t...-ACPurvaskuAAcGGWjIcM5Q@public.gmane.org> writes:

> First of all, thank you so much for taking the time to reply - really much
> appreciated, all the more given how busy I see you are, with so many
> awesome improvements.
> I love this "raw beamer" attribute, might make my document a lot more
> readable, yet to try it for other purposes.
> Unfortunately, this suggested solution does not help the issue at stake.
>
> The issue is for the content not to get forced slapped onto a slide.
> To create a new title page, I need the following piece of code:
> \mode<presentation>
> {
> \title[\CourseName{} Lecture 1]{\CourseName{} \newline \, Lecture 1}
> \date{\DayOne{}\Yr{}}
> }
> ###
> \titlepage
>
> And this {...} code cannot sit inside a frame or a latex error is thrown (!
> Illegal parameter number in definition of \iterate.).
> After 2.7 - there is no more option for me to write content outside a frame
> - everything is forced into a frame.
> "raw beamer" attribute does not escape this behavior unfortunately.
>
> Hence my suggestion last night - i don't know if that would be acceptable
> or even useful?
> But i have been thinking that I am perfectly fine with level -2 content not
> being forced onto slides.
> From what I read, it looks like reveal.js users only need level -1 content
> slapped onto slides?
> Of course, I'd be happy with any other solution you think is best.
>
> Many thank
> thomas
>
>
> On Tue, Aug 25, 2020 at 4:00 AM John MacFarlane <j...-TVLZxgkOlNX2fBVCVOL8/A@public.gmane.org> wrote:
>
>>
>> If you use the raw attribute to mark up content as "raw beamer,"
>> as suggested earlier in this thread, it will not appear in
>> reveal.js output. Demo here:
>>
>>
>> https://pandoc.org/try/?text=%23+Introduction%0A%0A%60%60%60%7B%3Dbeamer%7D%0AHey+this+is+raw+beamer!%0A%60%60%60%0A%0A%23%23+Slide+one%0A%0Acontent%0A%0A%23%23%23+Vertical+slide%0A%0Acontent+vertical%0A&from=markdown&to=revealjs&standalone=0
>>
>>
>> Thomas Chevrier <tch...-Re5JQEeQqe8AvxtiuMwx3w@public.gmane.org> writes:
>>
>> > Hi folks,
>> >
>> > it's been exactly a year now and I am still not able to upgrade my
>> version
>> > of Pandoc - stuck pre 2.7, because of the adverse change.
>> > Indeed, the "upgrade" for reveal.js users caused my latex beamer code to
>> > break down.
>> > I have tried multiple things without luck - I also tried a lua filter,
>> but
>> > that did not work - no matter what, the content gets "slapped" onto a
>> slide.
>> > As JGM suggests (was great watching him talk about Pandoc at TUG 2020
>> > keynote address), I'd love to be able to simply be able to have content
>> > escape being slapped onto a slide - I believe that's precisely the
>> spirit
>> > of Beamer, which uses <mode> heavily for that purpose.
>> > I also thought that was the spirit of pandoc - as you were setting in
>> the
>> > yaml header your level for displaying on slides, but i have been clearly
>> > proven wrong. :-(
>> > One option would be to recompile pandoc without that change, but because
>> of
>> > the bloomberg API, I am forced to be on windows, which would make this
>> > solution cumbersome at best (would be straightforward on linux though).
>> >
>> > FYI, I posted back then on SO, got only 2 upvotes and 2 bookmarks, but
>> no
>> > answer, not even a comment :-(
>> >
>> https://stackoverflow.com/questions/57614387/pandoc-4317-forces-content-under-title-slides-to-be-included-in-a-frame-in-pand
>> >
>> >
>> > Could anyone *please* help me?
>> > many thanks in advance
>> > thomas
>> >
>> >
>> > On Wednesday, August 28, 2019 at 12:23:15 AM UTC+8 John MacFarlane wrote:
>> >
>> >>
>> >> To summarize the issue here, which concerns a change to slide
>> >> show formats:
>> >>
>> >> Prior to 2.7, versions of pandoc only put material under the "slide
>> >> level" headings on slides. If you set slide level to 2, then
>> >> only material under level-2 headings would appear on slides,
>> >> and text under level-1 headings would not appear at all
>> >> (though level-1 headings would create "title slides" with
>> >> just the section title).
>> >>
>> >> Reveal.js users consistently complained (#4317, #5237) that
>> >> this made it hard to structure reveal.js 2D slide shows, in
>> >> which it is common to have the "top" slide on each column
>> >> contain both a title and some text.
>> >>
>> >> In response, I changed pandoc in 2.7 -- as the changelog says,
>> >>
>> >> > Slide show formats behavior change: content under headers less
>> >> > than slide level is no longer ignored, but included in the title
>> >> > slide (for HTML slide shows) or in a slide after the title slide
>> >> > (for beamer). This change makes possible 2D reveal.js slideshows
>> >> > with content in the top slide on each stack (#4317, #5237).
>> >>
>> >> The change to reveal.js has been welcomed by reveal.js users,
>> >> but the change to beamer is apparently not welcome by everyone.
>> >> The reason I made the change to both formats is because I want
>> >> slide shows to work the same no matter what output format you
>> >> use. (So you can switch from beamer to reveal.js, for example,
>> >> and the slides will look more or less the same.)
>> >>
>> >> I had thought the beamer change was innocuous, since it could
>> >> be worked around by people who wanted to include content under
>> >> top-level section headings but not in the slides, e.g. by using
>> >> a filter to strip out this content.
>> >>
>> >> Unfortunately, Thomas Chevrier's use case can't be handled that
>> >> way. He wants to insert raw tex commands that (a) can't be
>> >> stripped out but (b) only work if they're outside the
>> >> 'frame' environment created for a slide. I can't think of any
>> >> workaround for this.
>> >>
>> >> One possible course of action would be to revert the beamer
>> >> change while keeping the reveal.js change. This would potentially
>> >> have two bad consequences:
>> >>
>> >> 1) slide shows would render differently (in content, not just
>> >> form) in reveal.js and beamer.
>> >>
>> >> 2) this may break slide shows that were constructed using the
>> >> new behavior since 2.7 was released.
>> >>
>> >> A less radical change might be to introduce special Div whose
>> >> contents get moved outside the slide itself. Anyway, comments
>> >> welcome.
>> >>
>> >>
>> >>
>> >
>> > --
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>> .
>>

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