If both Judaism and Trinitariansm are monotheistic, Jesus being a jew, do both faiths have the same God?
If the word mono means one, single how can it be explained logically that 3 is 1 and 1 is 3?
Is God the source of fuzzy logic and numbers?
Monotheism requires one God who, alone, is worshipped. Judaism has but one God who, alone, is worshipped. Christianity has but one God who, alone, is worshipped.
For ease of understanding, compare that with the Hindu triad. It requires three gods who are all worshipped equally. But a triad is not a trinity, for the Christian trinity requires one God.
Your question would benefit from elaboration because monotheism is monotheism is monotheism. You add a comment in the form of a second question, "If both Judaism and Trinitariansm are monotheistic, Jesus being a jew, do both faiths have the same God?" Jesus being a Jew has nothing to do with either question.
Both Judaism and Christianity are clear that there is only one true God, who alone is to be worshipped. If one group has a more complex understanding of the nature of deity than the other, that does not necessarily mean one group cannot be worshipping the same God as the other group. All sincere worshippers of the only true God grow in their understanding as they keep seeking to learn about and to please God. Some are at one level of understanding, others are at another. Knowing God is a matter of divine revelation that comes in degrees; it is not about head-knowledge, or having theological degrees. God sovereignly chooses to whom, and to what extent, he reveals himself. That accounts for an awful lot of clashing theological beliefs about the nature of the one true God.
EDIT in response to your edit, "If the word mono means one, single how can it be explained logically that 3 is 1 and 1 is 3? Is God the source of fuzzy logic and numbers?"
Regarding Deuteronomy 6:4, this commentary notes:
"In Heb. shem'ayisrael y'hovah'eloheynuy'hovah echad = "Hear , O Israel, Jehovah [the Self and ever existing One), our Elohim, is one Jehovah."
one. Heb. 'ehad - a compound unity (Latin unus), one made up of others [Then gives 8 O.T. examples...] It is not yahid, which is (Latin) unicus, unique - a single, or only one [and gives 12 OT examples of that...]." (The Companion Bible notes p247)
Comment on this verse is worth quoting from another source:
"Some have thought there is here a plain intimation of the trinity of persons in the unity of the Godhead; for here is the name of God three times, and yet all declared to be one." (Matthew Henry Commentary, p192, 3rd column).
The Jewish and Christian God is not a numeric 'one', so the sooner people stop thinking that, the sooner they will see the logic of the trinity doctrine. It never was a case of 1 + 1 + 1 = 1 as scoffers love to say. Given that 1 x 1 x 1 = 1, numeracy should not be used to disagree with the trinity doctrine. It's not about numbers. It's about complex relationship within the Godhead. I hope that helps those who think the doctrine shows 'fuzzy logic', when it's fallible human logic that's the problem. Grasping the complexity of the one God, who alone is to be worshipped (as both Jews as trinitarian Christians adamantly maintain) requires divine revelation. That comes supremely in seeing just who Jesus the Messiah is. When Jewish people grasp that, they realise Christians have the same God as the God of the Shema of Deuteronomy 6:4.
do both faiths have the same God ?
No, because the inner moral character of these two Gods is completely different from one another. While formally or officially revering the Old Covenant and its deity, orthodox Christianity practically reinterprets the meaning and intention behind the actions and behavior of the Old Testament God (itself distinct from the post-biblical Jewish God), so as to render it more attuned with the One preached by its Founder.
The Old Testament, along with the Talmud, and the works of various post-Talmudic rabbis, such as Maimonides and Nachmanides, are in the public domain, in plain English; one can easily contrast and compare them with Christian morality, if one so desires.
Of course, non-orthodox forms of Christianity, such as Gnosticism, who repudiated the Old Testament and its deity, did indeed exist; but they were simply an excuse to indulge in otherwise pagan habits, forbidden, sometimes under penalty of death, by the Mosaic Covenant, as can be glimpsed from various surviving ancient patristic works, contemporary with the aforementioned movement, such as Irenaeus' Against Heresies and Augustine's anti-Gnostic writings, among others.
Generally speaking, Christianity chose to reinterpret old pre-Christian myths, legends, faiths, and religions, rather than brutally abolish them (which is why all Christian bibles still have an Old Testament); seeing Gnosticism's failed experiment, one can, in retrospect, better understand why this more diplomatic path was also much wiser and more successful than its alternate.
What is the the difference between Jewish monotheism and Trinitarian monotheism ?
Apart from reinterpreting Jewish morality, Christianity also reinterpreted Jewish theology; thus, the basic notion of divine unity was reinterpreted through the lens of passages such as Genesis 2:24 (quoted in Matthew 19:5-6, Mark 10:8, 1 Corinthians 6:16, Ephesians 5:31), especially in light of Genesis 1:26-27, this theme of familial unity being also echoed by John 10:30, with respect to Christ and His Father.
As I wrote elsewhere:
Let us recall that, while Adam (meaning Man) may not have been the only human in the Bible, he certainly is the only one to have borne the name of our entire species in his own person; with all of this in mind, let us now adduce the following reasoning: Just as Adam's (Man's) humanity does not infringe upon that of the beings descended from his own flesh and blood (Genesis 2:23), despite his being the only person in the entire Scripture to have ever borne the name Man as his own personal name, in virtue of his being the one father of all mankind, so also the divinity of the one God and Father does not necessarily deter other possible divine persons (personifying His various divine attributes, as Eve did with Adam's) from possibly sharing in the same divinity; notice also how the very next verse (Genesis 2:24) perfectly mirrors or resembles Christ's own idea of family unity, expressed in John 10:30.